Pith Number

pith:SOIROCOE

pith:2026:SOIROCOEITKCF2DVW3B4UMDNGM

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A combinatorial model for the canonical join complex of alt $\nu$-Tamari lattices

Matthias M\"uller

Alt ν-Tamari lattices have their canonical join complexes realized by a combinatorial model of paths or diagrams.

arxiv:2605.13770 v1 · 2026-05-13 · math.CO

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\usepackage{pith}
\pithnumber{SOIROCOEITKCF2DVW3B4UMDNGM}

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We introduce a combinatorial model that realizes the canonical join complex of alt ν-Tamari lattices. Serving as a universal tool, this model allows us to prove vertex decomposability, establish an explicit shelling order, and reveal the underlying homology of the canonical join complex of alt ν-Tamari lattices.

C2weakest assumption

That the proposed combinatorial objects (paths or diagrams) are in bijection with the canonical joins of the alt ν-Tamari lattice for every choice of ν, with no missing or extra faces.

C3one line summary

A combinatorial model for the canonical join complex of alt ν-Tamari lattices proves vertex decomposability, shellability, and computes the homology.

References

102 extracted · 102 resolved · 0 Pith anchors

[1] Wachs, M. L. , TITLE =. Discrete Comput. Geom. , FJOURNAL =. 1999 , NUMBER =. doi:10.1007/PL00009450 , URL = 1999 · doi:10.1007/pl00009450

[2] 2008 , doi = 2008

[4] 1951 , PAGES = 1951

[5] Order , year =

[6] Ceballos, Cesar and M\"uhle, Henri , TITLE =. Comb. Theory , FJOURNAL =. 2022 , NUMBER = 2022

Receipt and verification

First computed	2026-05-18T02:44:16.004160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93911709c444d422e875b6c3ca306d3336f46c529c010cc41f4d6ea06ed96e09

Aliases

arxiv: 2605.13770 · arxiv_version: 2605.13770v1 · doi: 10.48550/arxiv.2605.13770 · pith_short_12: SOIROCOEITKC · pith_short_16: SOIROCOEITKCF2DV · pith_short_8: SOIROCOE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SOIROCOEITKCF2DVW3B4UMDNGM \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 93911709c444d422e875b6c3ca306d3336f46c529c010cc41f4d6ea06ed96e09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d993223001910ca412e32e730c1767e88c829abd2a6cb54d3b3ee70e1c63759",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T16:48:28Z",
    "title_canon_sha256": "0476dc00665ef923c8c093e39b391ec6ea7eb0bdb19a063f13124a769a2b4f51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13770",
    "kind": "arxiv",
    "version": 1
  }
}