Catalan states of lattice crossing: an application of plucking

Mieczysław K. Dąbkowski , Józef Henryk Przytycki


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
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
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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