Pith Number

pith:QERSKWHG

pith:2026:QERSKWHGEEF6N7Q64GGT3IXBMS

not attested not anchored not stored refs resolved

Positivity of arbitrary-order P-recursive sequences with a unique dominant root

Zhongjie Li

A sufficient condition proves ultimate positivity for P-recursive sequences of any order with a unique dominant root.

arxiv:2605.17013 v1 · 2026-05-16 · math.CO

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\pithnumber{QERSKWHGEEF6N7Q64GGT3IXBMS}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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 establish a sufficient condition for the ultimate positivity of P-recursive sequences of arbitrary order with a unique dominant root.

C2weakest assumption

The sequence possesses a unique dominant root (i.e., one root of the characteristic equation strictly dominates all others in modulus), which is invoked as the structural hypothesis enabling the sufficient positivity condition.

C3one line summary

A sufficient condition is derived for ultimate positivity of arbitrary-order P-recursive sequences with a unique dominant root, allowing positivity to be settled by finite initial-term verification, with concrete examples for orders exceeding two.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] J.P. Bell and S. Gerhold, On the positivity set of a linear recurrence sequence, Israel J. Math.157(2006), 333–345. 13 2006

[2] T.W. Cusick, Recurrences for sums of powers of binomial coefficients, J. Combin. Theory Ser. A52(1989), 77–83 1989

[3] E. Deutsch and L. Shapiro, A survey of the Fine numbers, Discrete Math.241(2001), 241–265 2001

[4] V. Halava, T. Harju and M. Hirvensalo, Positivity of second order linear recurrent sequences, Discrete Appl. Math.154(2006), 447–451 2006

[5] A. Ibrahim and B. Salvy, Positivity Certificates for Linear Recurrences, Proc. 2024 Annu. ACM-SIAM Symp. Discrete Algorithms (SODA) (2024), 982–994 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:35.900875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81232558e6210be6fe1ee18d3da2e164af6ba0577b7faf8c8fc0236d7d1bb7d1

Aliases

arxiv: 2605.17013 · arxiv_version: 2605.17013v1 · doi: 10.48550/arxiv.2605.17013 · pith_short_12: QERSKWHGEEF6 · pith_short_16: QERSKWHGEEF6N7Q6 · pith_short_8: QERSKWHG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QERSKWHGEEF6N7Q64GGT3IXBMS \
  | 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: 81232558e6210be6fe1ee18d3da2e164af6ba0577b7faf8c8fc0236d7d1bb7d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da28ff9559cf407b5b0d2dad6817725d2dc978ab339b507f01a6ef735023e753",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-16T14:22:49Z",
    "title_canon_sha256": "f6bc61ee9f609334f774f458e22bb329281fb5460f1d8c73a0fdae2d3a2a3e9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17013",
    "kind": "arxiv",
    "version": 1
  }
}