Pith Number

pith:SIYD6NTK

pith:2026:SIYD6NTKN6333UTEQBTUDQ7XDO

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Hypermaps with hyperedges of length at most $3$

G\'abor Hetyei, Robert Cori

For hypermaps with hyperedges of length at most 3, the Whitney polynomial and spanning hypertree counts depend only on the underlying multi-hypergraph structure.

arxiv:2605.16741 v1 · 2026-05-16 · math.CO

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Claims

C1strongest claim

We develop deletion-contraction formulas involving six types of generalized loops and bridges, and we prove results on special substitutions into our Whitney polynomial for hypermaps whose hyperedges have length at most 3.

C2weakest assumption

The computation of the Whitney polynomial and the enumeration of spanning hypertrees for this class of hypermaps depends only on the underlying (multi)hypergraph structure rather than on the embedding.

C3one line summary

For hypermaps with hyperedges of length at most 3 the Whitney polynomial and spanning hypertrees depend only on the underlying hypergraph and admit deletion-contraction formulas; explicit counts are given for spanning hypertrees in reciprocals of maximum-degree-3 plane graphs.

References

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[1] R. Arratia, B. Bollob´ as and G.B. Sorkin, The interlace polynomial: a new graph polynomial, in: Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, CA, 2000), 2000

[2] Bernardi, A characterization of the Tutte polynomial via combinatorial embeddings,Ann 2008

[3] Bollob´ as, Evaluations of the circuit partition polynomial,J 2002

[4] Un code pour les Graphes Planaires et ses applications, 1975

[5] Cori, Codage d’une carte planaire et hyperarbres recouvrants, Colloques Internat 1976

Formal links

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Receipt and verification

First computed	2026-05-20T00:02:39.286520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92303f366a6fb7bdd264806741c3f71b886e4e226795959340dcd8100d861a31

Aliases

arxiv: 2605.16741 · arxiv_version: 2605.16741v1 · doi: 10.48550/arxiv.2605.16741 · pith_short_12: SIYD6NTKN633 · pith_short_16: SIYD6NTKN6333UTE · pith_short_8: SIYD6NTK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SIYD6NTKN6333UTEQBTUDQ7XDO \
  | 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: 92303f366a6fb7bdd264806741c3f71b886e4e226795959340dcd8100d861a31

Canonical record JSON

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    "abstract_canon_sha256": "3e461208e22b426c009818ec2b0a76d00bd3b2ce659643c0120de21541c15e5f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-16T01:37:54Z",
    "title_canon_sha256": "6488361d7b172340e479d2196d3e4cbc871526ed6956cabad8c6a0cb9320ac6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16741",
    "kind": "arxiv",
    "version": 1
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}