Pith Number

pith:OYFZNS7V

pith:2026:OYFZNS7VIQLNIEEFSK3WOFNRXE

not attested not anchored not stored refs resolved

Unimodality of $q$-Fibonomial coefficients for small cases

Brendan B. Connelly, Ezekiel Ito, Kacey Yang, Olha Shevchenko, Thomas C. Martinez

q-Fibonomial coefficients are unimodal for all n at most 3

arxiv:2605.12822 v1 · 2026-05-12 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OYFZNS7VIQLNIEEFSK3WOFNRXE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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 prove the conjecture for n≤3. For the n=2 case, we give a combinatorial proof of both unimodality and symmetry by defining a nearly symmetric saturated chain decomposition on the set of tilings.

C2weakest assumption

The weighted path-domino tiling model introduced by Bergeron--Ceballos--Küstner correctly interprets the q-Fibonomial coefficients and that the algebraic identities for q-analogs hold without additional restrictions for the small n considered.

C3one line summary

q-Fibonomial coefficients are unimodal for n≤3, with a combinatorial proof of unimodality and symmetry for n=2 via nearly symmetric saturated chain decompositions on tilings and algebraic proofs for n≤3.

References

19 extracted · 19 resolved · 0 Pith anchors

[1] Symmetry, Integrability and Geometry: Methods and Applications , language =

[2] Benjamin, Arthur and Quinn, Jennifer J. , address =

[3] 1989 , publisher = 1989

[4] 1878 , publisher =

[5] O'Hara, Kathleen M. , journal =. 1990 , publisher = 1990

Receipt and verification

First computed	2026-05-18T03:09:12.206552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

760b96cbf54416d4108592b76715b1b915806d27fb0ce81923073f67e5d05aac

Aliases

arxiv: 2605.12822 · arxiv_version: 2605.12822v1 · doi: 10.48550/arxiv.2605.12822 · pith_short_12: OYFZNS7VIQLN · pith_short_16: OYFZNS7VIQLNIEEF · pith_short_8: OYFZNS7V

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/OYFZNS7VIQLNIEEFSK3WOFNRXE \
  | 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: 760b96cbf54416d4108592b76715b1b915806d27fb0ce81923073f67e5d05aac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd678e3bd56cb01645c53faa3c527f77b91f317a848ea799750d84dce552f2eb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-12T23:44:53Z",
    "title_canon_sha256": "fce3a735b96973702fbd214aa60559cf751a51569c56ab413c75be4a3dd28b59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12822",
    "kind": "arxiv",
    "version": 1
  }
}