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On piecewise-linear homeomorphisms between distributive and anti-blocking polyhedra

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Christoph Pegel, Raman Sanyal

Combinatorics · Submitted 27 Nov 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We generalize Stanley's PL-homeomorphism to a large class of distributive polyhedra using infinite walks in marked networks.

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arXiv ID1911.12090 (version 1)
Pith IDXMGDJTPI, Pith's permanent record of this paper and its review
CitationChristoph Pegel, Raman Sanyal. "On piecewise-linear homeomorphisms between distributive and anti-blocking polyhedra." arXiv:1911.12090 (2019). https://pith.science/paper/XMGDJTPI
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,622 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. In this paper we view order and chain polytopes as instances of distributive and anti-blocking polytopes, respectively. Both these classes of polytopes are defined in terms of the componentwise partial order on $\mathbb R^n$. We generalize Stanley's PL-homeomorphism to a large class of distributive polyhedra using infinite walks in marked networks.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. background 1.00 0.02 0.04 asserted 1.00
s1 In this paper we view order and chain polytopes as instances of distributive and anti-blocking polytopes, respectively. contribution 0.60 0.84 0.07 asserted 1.00
s2 Both these classes of polytopes are defined in terms of the componentwise partial order on $\mathbb R^n$. background 1.00 0.14 0.03 asserted 1.00
s3 We generalize Stanley's PL-homeomorphism to a large class of distributive polyhedra using infinite walks in marked networks. contribution 0.96 0.95 0.85 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.99.

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  • references and citing sentences
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. In this paper we view order and chain polytopes as instances of distributive and anti-blocking polytopes, respectively. Both these classes of polytopes are defined in terms of the componentwise partial order on $\mathbb R^n$. We generalize Stanley's PL-homeomorphism to a large class of distributive polyhedra using infinite walks in marked networks.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 4 sentences without a confident label

Cites as background 1 paper
  • The $s$-lecture hall cones and polytopes of Bousquet-Mélou and Eriksson [ref] and Stanley's $P$-partitions [ref] were elegantly combined in [ref] to lecture hall order cones/polytopes.

    Lecture hall P-partitions · Lecture hall order cones and polytopes · 0.91

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