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Interval hypergraphic polytopes (or deformed associahedra), Tamari interval posets, and weeping willows

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Pith's one-line read Interval hypergraphs on [n] produce polytopes whose vertex posets are Tamari interval posets, with the simple cases having weeping willow posets.

desk verdict The paper gives explicit bijections showing interval hypergraphic polytopes have Tamari interval posets as vertex posets, with weeping willows for the simple cases. read the letter →

arxiv 2606.18376 v1 pith:MWKSCCQD submitted 2026-06-16 math.CO

Jose Bastidas , Félix Gélinas , Vincent Pilaud , Germain Poullot , Andrew Sack , Eleni Tzanaki This is my paper · ORCID
classification math.CO
keywords hypergraphicpolytopesintervalhypergraphsTamariposetsweepingwillowsassociahedrondeformationsMinkowskisumssimplevertex
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper examines hypergraphic polytopes obtained as Minkowski sums of standard simplices, one for each hyperedge in a hypergraph on the ground set [n]. When every hyperedge is required to be an interval, these polytopes become deformations of Loday's associahedron. Their vertices are labeled by Tamari interval posets, and the authors give an explicit description of which Tamari interval poset arises from which choice of interval hypergraph. They further single out the interval hypergraphs that make the resulting polytope simple and show that the vertex posets in those cases are a special family they name weeping willows.

What carries the argument

The explicit mapping from interval hypergraphs (hyperedges restricted to intervals of [n]) to Tamari interval posets realized as the vertex posets of the corresponding Minkowski-sum polytopes.

What would settle it

An explicit interval hypergraph on a small n whose computed vertices do not form a Tamari interval poset, or a simple interval hypergraphic polytope whose vertex poset is not a weeping willow.

Watch

Extended reading notes

Core claim

For any interval hypergraph on [n], the associated hypergraphic polytope is a deformation of Loday's associahedron whose vertex poset is a Tamari interval poset. The interval hypergraphs for which this polytope is simple have vertex posets that are weeping willows.

Load-bearing premise

Restricting hyperedges to intervals on [n] is enough to guarantee that the hypergraphic polytope deforms Loday's associahedron and that its vertices correspond to Tamari interval posets.

Editorial extensions

If this is right

  • Every choice of interval hypergraph on [n] yields a hypergraphic polytope whose vertices are labeled by a Tamari interval poset.
  • The simple interval hypergraphic polytopes are precisely those whose vertex posets belong to the weeping willow family.
  • Different interval hypergraphs produce different Tamari interval posets as their vertex posets.
  • The geometric properties of the polytope, such as simplicity, translate directly into combinatorial restrictions on the corresponding Tamari interval poset.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The construction supplies a geometric model in which combinatorial operations on Tamari interval posets can be studied via Minkowski sums and face lattices of polytopes.
  • One could test whether non-interval hypergraphs ever produce Tamari interval posets or whether the interval restriction is necessary for the correspondence.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 2 minor

Summary. The paper defines interval hypergraphic polytopes as Minkowski sums of standard simplices over interval hyperedges on [n]. It establishes that these are precisely the deformations of Loday's associahedron, proves that their vertex posets coincide with Tamari interval posets via explicit bijections, describes the correspondence between specific interval hypergraphs and Tamari interval posets, characterizes the interval hypergraphs yielding simple polytopes, and names the vertex posets of the simple cases 'weeping willows'.

Significance. If the explicit bijections and characterizations hold as described, the work supplies a direct combinatorial link between hypergraphic polytopes, deformations of the associahedron, and Tamari interval posets. The step-by-step development from the Minkowski-sum definition to the poset identifications strengthens the contribution to algebraic combinatorics and polytope theory.

minor comments (2)
  1. The abstract and introduction would benefit from a brief statement of the main theorem numbers that establish the bijection between vertices and Tamari interval posets.
  2. Notation for the interval hypergraph I and the resulting polytope triangle_I is introduced early; a consolidated table of symbols in an appendix would aid readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of the manuscript and for recommending minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation self-contained from Minkowski sums and poset definitions

full rationale

The paper defines hypergraphic polytopes via Minkowski sums of simplices over interval hypergraphs, then proves (via explicit bijections and characterizations in the full manuscript) that their vertex posets are Tamari interval posets and identifies the simple cases as weeping willows. No step reduces a claimed result to a fitted parameter, self-citation load-bearing premise, or definitional renaming; the identifications follow from combinatorial constructions starting from the Minkowski-sum definition without circular reduction. The abstract's statements are supported by step-by-step proofs rather than presupposing the conclusions.

Assumptions & free parameters 0 free parameters · 1 assumptions · 1 invented entities

The paper relies on standard properties of Minkowski sums and convex polytopes; no free parameters or new invented entities beyond the naming of weeping willows are visible in the abstract.

assumptions (1)
  • standard math Minkowski sum of simplices yields a polytope whose vertices correspond to selections of one vertex from each summand
    Basic fact of convex geometry invoked to define hypergraphic polytopes
invented entities (1)
  • weeping willows
    purpose: Name for the vertex posets of simple interval hypergraphic polytopes
    New descriptive term introduced for the characterized objects

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Pith. "Pith review of Interval hypergraphic polytopes (or deformed associahedra), Tamari interval posets, and weeping willows." pith.science (2026). https://pith.science/paper/MWKSCCQD

@misc{pith2026260618376,
  author       = {Pith},
  title        = {Pith review of: Interval hypergraphic polytopes (or deformed associahedra), Tamari interval posets, and weeping willows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MWKSCCQD}},
  note         = {Machine review of arXiv:2606.18376}
}
abstract

For a hypergraph $\mathbb{H}$ on $[n]$, the hypergraphic polytope $\triangle_{\mathbb{H}}$ is the Minkowski sum of the standard simplices $\triangle_H$ for all $H \in \mathbb{H}$. We focus here on interval hypergraphs, where all hyperedges are intervals of $[n]$. They are precisely the deformations of Loday's associahedron. Their vertex posets are Tamari interval posets, and we describe which Tamari interval poset appears as a vertex poset in which interval hypergraphic polytope. We also characterize the interval hypergraphs $\mathbb{I}$ for which the hypergraphic polytope $\triangle_\mathbb{I}$ is simple, and we study their vertex posets, which we call weeping willows.

Figures

Figures reproduced from arXiv: 2606.18376 by the authors.

Figure 1
Figure 1. The main families of hypergraphic polytopes discussed in this paper. VP was supported by the Spanish project PID2022-137283NB-C21 of MCIN/AEI/10.13039/501100011033 / FEDER, UE, by the Spanish–German project COMPOTE (AEI PCI2024-155081-2 & DFG 541393733), and by the Severo Ochoa and Mar´ıa de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). 1 arXiv:2606.18376v1 [math.CO] 16 Jun 2026 [PIT… view at source ↗
Figure 2
Figure 2. Examples of 3-dimensional hypergraphic polytopes [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. (Left) An interval hypergraph I, (Right) and the graph formed by the directed edges (O4132(H), h) for each H ∈ I and each h ∈ H \ {O4132(H)}. Proof. If there exist I, J ∈ I such that O(I) ∩ J ̸= ∅ and O(J) ∩ (I ∖ O(I)) ̸= ∅, then O is cyclic by Definition 2.9. Conversely, suppose that O is cyclic, and let I1, . . . , Ik ∈ I be such that there are x1 ∈ O(I1)∩(Ik ∖{O(Ik)}) and xi ∈ O(Ii)∩Ii−1 for 2 ≤ i ≤ k, and that k… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: Plumbing bijection. (ii) the interval hypergraphs of (ii) are called union closed and are precisely (up to the singletons) the interval building sets in the sense of [FS05, Pos09], and their hypergraphic polytopes are interval nestohedra (in particular, they are simple…
Figure 5
Figure 5. Figure 5: The boolean lattice I of interval hypergraphs (containing all sin￾gletons) on 4 nodes, with respect to inclusion. We encode a hypergraph by a subset of the triangle, where the presence of an interval [i, j] appears as a solid dot in diagonal i and antidiagonal j − 1. F…
Figure 6
Figure 6. Figure 6: Diamond and crown posets. However, searching in general for patterns in H which yield vertex digraphs of △H containing the cycles of Lemma 3.15 seems combinatorially intricate and computationally inefficient. We thus leave the following problem open. Problem 3.17. What…
Figure 7
Figure 7. Figure 7: The Hasse diagram of a typical Tamari interval poset. 4.2. Two families of Tamari interval posets. We describe two interesting families of Tamari interval posets, which will later appear as the vertex posets of certain families of hypergraphic polytopes (see also Secti…
Figure 8
Figure 8. Figure 8: An interval hypergraph I with a Tamari interval poset associated to the vertex v of △I . By Proposition 4.17, counting the number of intervals of I with minimum element i for each i ∈ [9] yields v = (1, 0, 0, 1, 0, 0, 2, 1, 0) Proposition 4.17. The vertex of an interva…
Figure 9
Figure 9. Figure 9: The interval hypergraphs I◁ (left) and J◁ (right) for the Tamari interval poset ◁ drawn on top. We did not draw the singletons they contain. The vertex corresponding to ◁ is v◁ = (2, 1, 1, 2, 1, 1, 2, 2, 1) in the polytope △I◁ and v◁ = (6, 1, 1, 3, 1, 1, 5, 12, 1) in t…
Figure 10
Figure 10. Figure 10: The boolean lattice I of interval hypergraphs on 4 nodes (see Fig￾ure 5 for the encoding and color conventions: red yield non-simple interval hyper￾graphic polytopes; blue and green yield simple ones; green yield nestohedra), we have encircled (in orange) the interval…
Figure 11
Figure 11. Figure 11: A typical weeping willow. The crown arcs are (10, 1),(10, 18) and (24, 18). In contrast, U(◁) contains all cover relations except 5◁· 4, 10◁· 8, 10◁· 11, 10 ◁· 14 and 24 ◁· 22. In our figures, the crown arcs are the topmost arcs. In particular, every crown arc is a co…
Figure 12
Figure 12. Figure 12: Illustration for the proof of Proposition 5.12. Proof. We refer the reader to [PITH_FULL_IMAGE:figures/full_fig_p029_12.png]
Figure 13
Figure 13. Figure 13: The two possible decomposition of the weeping willows described in Proposition 5.23 (ii). Red crosses ✖ indicate forbidden arcs. Remark 5.26. For the transitive closure ◁ of a weeping willow, the condition of Proposi￾tion 5.23 (ii) clearly implies the condition of Pro…
Figure 14
Figure 14. Figure 14: A typical Tamari interval preposet. 6.2. Inclusion versus refinement. Denote by C◀ := {x ∈ R n | xi ≥ xj if i ◀ j} the cone of a preposet ◀ on [n]. One can compare two preposets ◀ and ◀′ on [n] in two natural ways: • either by inclusion: C◀ ⊆ C◀′ , that is, i ◀′ j imp…
Figure 15
Figure 15. Figure 15: A typical Schr¨oder weeping willow. Definition 7.1. A Schr¨oder weeping willow on [n] is a directed tree SWW on a partition of [n] whose associated preposet is a Tamari interval preposet. Remark 7.2. The weeping willows of Definition 5.1 are essentially the Schr¨oder …
Figure 16
Figure 16. Figure 16: The lattice of Schr¨oder weeping willows on 3 nodes (trimmed of its artificial minimum) admits 14 elements. Proof. As a Schr¨oder weeping willow is a tree, the cone C◀ associated to some Schr¨oder weeping willow SWW is a simplicial cone. Consider two such simplicial c…
Figure 17
Figure 17. Figure 17: Decomposition for E (top left), for F (top middle), for G (top right), and for H (bottom). Substituting the formula expressing F in the formula for E gives the claimed annihilating polynomial for E. Once this is established, one can express F, G and H as functions of …

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Reference graph

Works this paper leans on

83 extracted references · 3 canonical work pages

  1. [1]

    Postnikov, Alexander , TITLE =. Int. Math. Res. Not. IMRN , FJOURNAL =. 2009 , NUMBER =

    2009

  2. [2]

    , TITLE =

    Postnikov, Alexander and Reiner, Victor and Williams, Lauren K. , TITLE =. Doc. Math. , FJOURNAL =. 2008 , PAGES =

    2008

  3. [3]

    Combinatorial

    Edmonds, Jack , TITLE =. Combinatorial

  4. [4]

    Feichtner, Eva Maria and Sturmfels, Bernd , TITLE =. Port. Math. (N.S.) , FJOURNAL =. 2005 , NUMBER =

    2005

  5. [5]

    Benedetti, Carolina and Bergeron, Nantel and Machacek, John , TITLE =. J. Comb. , FJOURNAL =. 2019 , NUMBER =

    2019

  6. [6]

    European J

    Bergeron, Nantel and Pilaud, Vincent , TITLE =. European J. Combin. , FJOURNAL =. 2026 , PAGES =

    2026

  7. [7]

    Discrete Comput

    Pilaud, Vincent and Poullot, Germain , TITLE =. Discrete Comput. Geom. , FJOURNAL =

  8. [8]

    and Devadoss, Satyan L

    Carr, Michael P. and Devadoss, Satyan L. , TITLE =. Topology Appl. , FJOURNAL =. 2006 , NUMBER =

    2006

Show all 83 references
  1. [9]

    Algebra Universalis , FJOURNAL =

    Barnard, Emily and McConville, Thomas , TITLE =. Algebra Universalis , FJOURNAL =. 2021 , NUMBER =

    2021

  2. [10]

    and Pitman, Jim , TITLE =

    Stanley, Richard P. and Pitman, Jim , TITLE =. Discrete Comput. Geom. , FJOURNAL =. 2002 , NUMBER =

    2002

  3. [11]

    Topology Appl

    Saneblidze, Samson , TITLE =. Topology Appl. , FJOURNAL =. 2009 , NUMBER =

    2009

  4. [12]

    Pilaud, Vincent and Poliakova, Daria , TITLE =. Math. Ann. , FJOURNAL =. 2025 , NUMBER =

    2025

  5. [13]

    Discrete Comput

    Defant, Colin , TITLE =. Discrete Comput. Geom. , FJOURNAL =. 2023 , NUMBER =

    2023

  6. [14]

    Pilaud, Vincent , TITLE =. Ann. Comb. , FJOURNAL =

  7. [15]

    Discrete Comput

    Kim, Sangwook , TITLE =. Discrete Comput. Geom. , FJOURNAL =. 2008 , NUMBER =

    2008

  8. [16]

    Permutation statistics and linear extensions of posets , VOLUME =

    Bj. Permutation statistics and linear extensions of posets , VOLUME =. J. Combin. Theory Ser. A , NUMBER =

  9. [17]

    Algebraic Combinatorics , PUBLISHER =

    Chatel, Gr\'egory and Pilaud, Vincent and Pons, Viviane , TITLE =. Algebraic Combinatorics , PUBLISHER =. 2019 , PAGES =

    2019

  10. [18]

    Counting smaller elements in the

    Ch. Counting smaller elements in the. J. Combin. Theory Ser. A , Pages =

  11. [19]

    Sur le nombre d'intervalles dans les treillis de

    Chapoton, Fr\'. Sur le nombre d'intervalles dans les treillis de. S\'. 2005/07 , PAGES =

    2005

  12. [20]

    Une note sur les intervalles de

    Chapoton, Fr\'. Une note sur les intervalles de. Ann. Math. Blaise Pascal , FJOURNAL =. 2018 , NUMBER =

    2018

  13. [21]

    Bernardi, Olivier and Bonichon, Nicolas , TITLE =. J. Combin. Theory Ser. A , FJOURNAL =. 2009 , NUMBER =

    2009

  14. [22]

    Tamari intervals and blossoming trees , JOURNAL =

    Fang, Wenjie and Fusy, \'. Tamari intervals and blossoming trees , JOURNAL =. 2025 , NUMBER =

    2025

  15. [23]

    Schoute, Pieter Hendrik , TITLE =

  16. [24]

    Rado, Richard , TITLE =. J. London Math. Soc. , FJOURNAL =. 1952 , PAGES =

    1952

  17. [25]

    Celebrating

    Pilaud, Vincent and Santos, Francisco and Ziegler, G\". Celebrating. Arch. Math. (Basel) , FJOURNAL =. 2023 , NUMBER =

    2023

  18. [26]

    Tamari, Dov , TITLE =

  19. [27]

    Loday, Jean-Louis , TITLE =. Arch. Math. (Basel) , FJOURNAL =. 2004 , NUMBER =

    2004

  20. [28]

    Operads:

    Tonks, Andy , TITLE =. Operads:

  21. [29]

    1993 , PAGES =

    Shnider, Steve and Sternberg, Shlomo , TITLE =. 1993 , PAGES =

    1993

  22. [30]

    Reading, Nathan , TITLE =. SIAM J. Discrete Math. , FJOURNAL =. 2015 , NUMBER =

    2015

  23. [31]

    Order , FJOURNAL =

    Reading, Nathan , TITLE =. Order , FJOURNAL =. 2004 , NUMBER =

    2004

  24. [32]

    Reading, Nathan , TITLE =. Adv. Math. , FJOURNAL =. 2006 , NUMBER =

    2006

  25. [33]

    Pilaud, Vincent and Santos, Francisco , TITLE =. Bull. Lond. Math. Soc. , FJOURNAL =. 2019 , VOLUME =

    2019

  26. [34]

    Padrol, Arnau and Pilaud, Vincent and Ritter, Julian , TITLE =. Int. Math. Res. Not. IMRN , FJOURNAL =. 2023 , NUMBER =

    2023

  27. [35]

    European J

    Pilaud, Vincent and Santos, Francisco , TITLE =. European J. Combin. , FJOURNAL =. 2012 , NUMBER =

    2012

  28. [36]

    Geometriae Dedicata , FJOURNAL =

    McMullen, Peter , TITLE =. Geometriae Dedicata , FJOURNAL =. 1973 , PAGES =

    1973

  29. [37]

    Padrol, Arnau and Palu, Yann and Pilaud, Vincent and Plamondon, Pierre-Guy , TITLE =. Proc. London Math. Soc. , FJOURNAL =. 2023 , NUMBER =

    2023

  30. [38]

    European J

    Padrol, Arnau and Pilaud, Vincent and Poullot, Germain , TITLE =. European J. Combin. , FJOURNAL =. 2023 , PAGES =

    2023

  31. [39]

    Electron

    Albertin, Doriann and Pilaud, Vincent and Ritter, Julian , TITLE =. Electron. J. Combin. , FJOURNAL =. 2021 , NUMBER =

    2021

  32. [40]

    Bazier-Matte, V\'eronique and Chapelier-Laguet, Nathan and Douville, Guillaume and Mousavand, Kaveh and Thomas, Hugh and Y. J. Lond. Math. Soc. (2) , FJOURNAL =. 2023 , DOI =

    2023

  33. [41]

    1970 , PAGES =

    Stasheff, James , TITLE =. 1970 , PAGES =

    1970

  34. [42]

    1997 , publisher=

    Enumerative Combinatorics: Volume 1 , author=. 1997 , publisher=

    1997

  35. [43]

    Topology Appl

    Forcey, Stefan , TITLE =. Topology Appl. , FJOURNAL =. 2008 , NUMBER =

    2008

  36. [44]

    Homology Homotopy Appl

    Saneblidze, Samson and Umble, Ronald , TITLE =. Homology Homotopy Appl. , FJOURNAL =. 2004 , NUMBER =

    2004

  37. [45]

    Ardila, Federico and Doker, Jeffrey , TITLE =. Adv. in Appl. Math. , FJOURNAL =. 2013 , NUMBER =

    2013

  38. [46]

    Shuffles of deformed permutahedra, multiplihedra, constrainahedra, and biassociahedra , JOURNAL =

    Chapoton, Fr\'. Shuffles of deformed permutahedra, multiplihedra, constrainahedra, and biassociahedra , JOURNAL =. 2024 , PAGES =

    2024

  39. [47]

    Bottman, Nathaniel and Poliakova, Daria , TITLE =

  40. [48]

    Source characterization of the hypergraphic posets , NOTE =

    G. Source characterization of the hypergraphic posets , NOTE =

  41. [49]

    Aguiar, Marcelo and Ardila, Federico , TITLE =. Mem. Amer. Math. Soc. , FJOURNAL =. 2023 , NUMBER =

    2023

  42. [50]

    Discrete Comput

    Padrol, Arnau and Pilaud, Vincent and Poullot, Germain , TITLE =. Discrete Comput. Geom. , FJOURNAL =. 2025 , NUMBER =

    2025

  43. [51]

    Padrol, Arnau and Pilaud, Vincent and Poullot, Germain , TITLE =. S\'. 2022 , PAGES =

    2022

  44. [52]

    Electron

    Rehberg, Sophie , TITLE =. Electron. J. Combin. , FJOURNAL =. 2022 , NUMBER =

    2022

  45. [53]

    and Merino, Arturo and Mi

    Cardinal, Jean and Hoang, Hung P. and Merino, Arturo and Mi. Combinatorial generation via permutation languages. SIAM J. Discrete Math. , FJOURNAL =. 2023 , NUMBER =

    2023

  46. [54]

    Cardinal, Jean and Steiner, Raphael , TITLE =. Comb. Theory , FJOURNAL =. 2025 , NUMBER =

    2025

  47. [55]

    , TITLE =

    Agnarsson, Geir and Morris, Walter D. , TITLE =. Ann. Comb. , FJOURNAL =. 2009 , NUMBER =

    2009

  48. [56]

    Electron

    Agnarsson, Geir , TITLE =. Electron. J. Combin. , FJOURNAL =. 2017 , NUMBER =

    2017

  49. [57]

    Ornamentation lattices and intreeval hypergraphic lattices , NOTE =

    Abram, Antoine and Bastidas, Jose and G. Ornamentation lattices and intreeval hypergraphic lattices , NOTE =

  50. [58]

    Proceedings of the NATO Advanced Study Institute held in Berlin (West Germany) , SERIES =

    Greene, Curtis , TITLE =. Proceedings of the NATO Advanced Study Institute held in Berlin (West Germany) , SERIES =

  51. [59]

    Greene, Curtis and Zaslavsky, Thomas , TITLE =. Trans. Amer. Math. Soc. , FJOURNAL =. 1983 , NUMBER =

    1983

  52. [60]

    , TITLE =

    Stanley, Richard P. , TITLE =. Discrete Math. , FJOURNAL =. 1973 , PAGES =

    1973

  53. [61]

    Selecta Math

    De Concini, Conrado and Procesi, Claudio , TITLE =. Selecta Math. (N.S.) , FJOURNAL =. 1995 , NUMBER =

    1995

  54. [62]

    Hypergraph polytopes , JOURNAL =

    Do. Hypergraph polytopes , JOURNAL =. 2011 , NUMBER =

    2011

  55. [63]

    Pilaud, Vincent , TITLE =

  56. [64]

    Knutson, Allen and Miller, Ezra , TITLE =. Adv. Math. , FJOURNAL =. 2004 , NUMBER =

    2004

  57. [65]

    Knutson, Allen and Miller, Ezra , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2005 , NUMBER =

    2005

  58. [66]

    Discrete Geometry and Optimization , PUBLISHER =

    Pilaud, Vincent and Stump, Christian , TITLE =. Discrete Geometry and Optimization , PUBLISHER =. 2013 , PAGES =

    2013

  59. [67]

    European J

    Froese, Vincent and Renken, Malte , TITLE =. European J. Combin. , FJOURNAL =. 2024 , PAGES =

    2024

  60. [68]

    Discrete Math

    Dumont, Dominique and Randrianarivony, Arthur , TITLE =. Discrete Math. , FJOURNAL =. 1994 , NUMBER =

    1994

  61. [69]

    On grounded

    Jel\'. On grounded. Electron. J. Combin. , FJOURNAL =. 2019 , NUMBER =

    2019

  62. [70]

    Proceedings of the 35th European Workshop on Computational Geometry (EuroCG) , PAGES =

    Ashur, Stav and Filtser, Omrit and Sababn, Rachel , TITLE =. Proceedings of the 35th European Workshop on Computational Geometry (EuroCG) , PAGES =

  63. [71]

    Discrete Comput

    Froese, Vincent and Renken, Malte , TITLE =. Discrete Comput. Geom. , FJOURNAL =. 2021 , NUMBER =

    2021

  64. [72]

    Hixon, Thomas Stuart , TITLE =

  65. [73]

    Discrete Math

    Soto, Mauricio and Thraves Caro, Christopher , TITLE =. Discrete Math. Theor. Comput. Sci. , FJOURNAL =. 2015 , NUMBER =

    2015

  66. [74]

    Max point-tolerance graphs , JOURNAL =

    Catanzaro, Daniele and Chaplick, Steven and Felsner, Stefan and Halld\'. Max point-tolerance graphs , JOURNAL =. 2017 , NUMBER =

    2017

  67. [75]

    Involve , FJOURNAL =

    Clark, Tyler and Richmond, Tom , TITLE =. Involve , FJOURNAL =. 2015 , NUMBER =

    2015

  68. [76]

    2026 , eprint=

    Indecomposability and beyond via the graph of edge dependencies , author=. 2026 , eprint=

    2026

  69. [77]

    2025 , eprint=

    Rays of the deformation cones of graphical zonotopes , author=. 2025 , eprint=

    2025

  70. [78]

    , TITLE =

    Wilf, Herbert S. , TITLE =. 1986 , PAGES =

    1986

  71. [79]

    Electron

    Bostan, Alin and Chyzak, Fr\'ed\'eric and Pilaud, Vincent , TITLE =. Electron. J. Combin. , FJOURNAL =. 2026 , NUMBER =. doi:10.37236/14666 , URL =

    2026 doi

  72. [80]

    Dermenjian, Aram and Hohlweg, Christophe and Pilaud, Vincent , TITLE =. Trans. Amer. Math. Soc. , FJOURNAL =. 2018 , NUMBER =. doi:10.1090/tran/7307 , URL =

    2018 doi

  73. [81]

    2026 , eprint=

    Dyck Paths, Configuration Spaces and Polytopes For Linear Nakayama algebras , author=. 2026 , eprint=

    2026

  74. [82]

    Arkani-Hamed, Nima and Bai, Yuntao and He, Song and Yan, Gongwang , TITLE =. J. High Energy Phys. , FJOURNAL =. 2018 , NUMBER =. doi:10.1007/jhep05(2018)096 , URL =

    2018 doi

  75. [83]

    2026 , eprint=

    Many rays of the submodular cone , author=. 2026 , eprint=

    2026

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