Catalan states of lattice crossing: an application of plucking

Mieczysław K. Dąbkowski , Józef Henryk Przytycki

Abstract

For a Catalan state C of a lattice crossing with no returns on one side, we find its coefficient in the Relative Kauffman Bracket Skein Module expansion of . We show, in particular, that can be found using the plucking polynomial of a rooted tree with a delay function associated to C. Furthermore, for C with returns on one side only, we prove that is a product of Gaussian polynomials, and its coefficients form a unimodal sequence.
Author Mieczysław K. Dąbkowski
Mieczysław K. Dąbkowski,,
-
, Józef Henryk Przytycki (FMPI / IM)
Józef Henryk Przytycki,,
- Institute of Mathematics
Journal seriesTopology and its Applications, ISSN 0166-8641, e-ISSN 1879-3207, (N/A 70 pkt)
Issue year2019
Vol254
Pages12-28
Publication size in sheets0.8
Keywords in EnglishCatalan states, Gaussian polynomial, knot, Kauffman bracket, link, lattice crossing, plucking polynomial, rooted tree, skein module, unimodal polynomial
ASJC Classification2608 Geometry and Topology
DOIDOI:10.1016/j.topol.2018.12.003
URL https://doi.org/10.1016/j.topol.2018.12.003
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 28-01-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.051; WoS Impact Factor: 2018 = 0.416 (2) - 2018=0.438 (5)
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