Pith Number

pith:MAGN2P3U

pith:2026:MAGN2P3UDLQT2RQBUU2GXZON7H

not attested not anchored not stored refs resolved

On groups with D-finite cogrowth series

Andrew Rechnitzer, Mudit Aggarwal, Murray Elder

An infinite family of groups has D-finite non-algebraic cogrowth series.

arxiv:2605.12793 v1 · 2026-05-12 · math.CO · math.GR

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Claims

C1strongest claim

we give a particular infinite family of presentations for which the cogrowth series can be determined as the constant term of an algebraic function, which shows that it is D-finite and, with more work, not algebraic.

C2weakest assumption

for a particular choice of subgroup, the corresponding Schreier graph has finite tree width, and by considering paths in the cosets and the Schreier graph separately, we are able to construct a system of generating functions which count paths.

C3one line summary

An infinite family of groups has D-finite but non-algebraic cogrowth series, constructed as constant terms of algebraic functions via generating functions on finite-treewidth Schreier graphs.

References

41 extracted · 41 resolved · 0 Pith anchors

[1] Scaling limits of permutation classes with a finite specification: A dichotomy 2022

[2] Cogrowth series for free products of finite groups 2023

[3] On the complexity of the cogrowth sequence.J 2020

[4] Submaps of maps 1992

[5] On groups whose cogrowth series is the diagonal of a rational series.Internat 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:12.870918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

600cdd3f741ae13d4601a5346be5cdf9c73ef021e474939811a4c6cbe1b1f693

Aliases

arxiv: 2605.12793 · arxiv_version: 2605.12793v1 · doi: 10.48550/arxiv.2605.12793 · pith_short_12: MAGN2P3UDLQT · pith_short_16: MAGN2P3UDLQT2RQB · pith_short_8: MAGN2P3U

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MAGN2P3UDLQT2RQBUU2GXZON7H \
  | 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: 600cdd3f741ae13d4601a5346be5cdf9c73ef021e474939811a4c6cbe1b1f693

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d96867a94cfddfab310b4d70639b77e59590ad88591d08169ff7f66b25ca018c",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-12T22:14:53Z",
    "title_canon_sha256": "d3d0decc77ca09fb7cc568642cfaaef649c9871f2325621cf43ca16cac3fd72f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12793",
    "kind": "arxiv",
    "version": 1
  }
}