Pith. sign in

REVIEW 1 cited by

The Hilbert Polynomial of Quandles and Colorings of Random Links

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2304.08314 v1 pith:URHCFXHE submitted 2023-04-17 math.GT

classification math.GT
keywords polynomialstabilitycoloringscomputednumberquandlequandlesrandom
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Given a finite quandle $Q$, we study the average number of $Q$-colorings of the closure of a random braid in $B_n$ as $n$ varies. In particular we show that this number coincides with some polynomial $P_Q\in \mathbb{Q}[x]$ for $n\gg 0$. The degree of this polynomial is readily computed in terms of $Q$ as a quandle and these invariants are computed for all quandles with $|Q|\le 4$. Additionally we show that the methods in this paper allow to improve on the stability results of arXiv:0912.0325 from "periodic stability" to "stability".

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Representation stability for ordered Hurwitz spaces

    math.AT 2025-09 conditional novelty 7.0 of 10

    The homology groups of ordered Hurwitz spaces, seen as representations of symmetric groups, have stable multiplicities in a range that grows linearly with homological degree.

Pith tools