Pith Number

pith:E33VGLXK

pith:2026:E33VGLXKPOIHJBFKVAHCS6XF3V

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On Some Properties of LCM-Lattices of Edge Ideals of k-Uniform Hypergraphs

Muneeba Mansha, Sarfraz Ahmad

The lcm-lattice of an edge ideal of a k-uniform hypergraph is Boolean, modular, or complemented under stated conditions on its edges.

arxiv:2605.13617 v1 · 2026-05-13 · math.AC

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Claims

C1strongest claim

We establish conditions under which the lcm-lattice of an edge ideal is Boolean, modular, or complemented. Furthermore, we extend these results to the case of the product of lcm-lattices in the complemented case.

C2weakest assumption

The hypergraph is k-uniform and the stated combinatorial conditions on its edges suffice to force the lattice-theoretic properties; the proofs rely on the standard correspondence between monomial generators and hypergraph edges without additional hidden restrictions on the ground set or characteristic.

C3one line summary

Conditions are established for lcm-lattices of edge ideals of k-uniform hypergraphs to be Boolean, modular, or complemented, with extensions to products and polarization effects.

References

12 extracted · 12 resolved · 1 Pith anchors

[1] Birkhoff, G. (1967). Lattice theory, vol. XXV. In American Mathematical Society Colloquium Publications, Providence, RI 1967

[2] A., & Priestley, H 2002

[3] Properties of LCM Lattices of Monomial Ideals 2025 · arXiv:2505.08722

[4] Dorang, M. T. (2025). Characterizations of edge ideals via LCM lattices (Master’s thesis, Iowa State University) 2025

[5] Faridi, S. (2019). Lattice complements and the subadditivity of syzygies of simplicial forests. Journal/Conference, 535-546 2019

Receipt and verification

First computed	2026-05-18T02:44:17.959881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26f7532eea7b907484aaa80e297ae5dd52daba3a0c7e453370221aa9716f7d53

Aliases

arxiv: 2605.13617 · arxiv_version: 2605.13617v1 · doi: 10.48550/arxiv.2605.13617 · pith_short_12: E33VGLXKPOIH · pith_short_16: E33VGLXKPOIHJBFK · pith_short_8: E33VGLXK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/E33VGLXKPOIHJBFKVAHCS6XF3V \
  | 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: 26f7532eea7b907484aaa80e297ae5dd52daba3a0c7e453370221aa9716f7d53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bf8e788d8e8089598c3a656a0fd1135fc2295fa6d5ded43575175ae7973dc7d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-05-13T14:46:34Z",
    "title_canon_sha256": "693e6be0b1b678c8da263a68f778928f5ecd1ecabbf1b1ddd1c60b2e2ef4d8b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13617",
    "kind": "arxiv",
    "version": 1
  }
}