Bilinear forms on skein modules and steps in Dyck paths

Xuanting Cai; Toufik Mansour

doi:10.1063/1.3609231

Bilinear forms on skein modules and steps in Dyck paths

Xuanting Cai, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We use Jones-Wenzl idempotents to construct bases for the relative Kauffman bracket skein module of a square with n points colored 1 and one point colored h. We consider a natural bilinear form on this skein module. We calculate the determinant of the matrix for this form with respect to the natural basis. We reduce the computation to count some steps in generalized Dyck paths. Moreover, we relate our determinant to a determinant on semi-meanders.

Original language	English
Article number	073509
Journal	Journal of Mathematical Physics
Volume	52
Issue number	7
DOIs	https://doi.org/10.1063/1.3609231
State	Published - 11 Jul 2011

Bibliographical note

Funding Information:
The first author thanks his advisor Professor Patrick Gilmer for helpful discussions. The first author was partially supported by research assistantship funded by National Science Foundation (NSF)-DMS-0905736.

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.3609231

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abstract = "We use Jones-Wenzl idempotents to construct bases for the relative Kauffman bracket skein module of a square with n points colored 1 and one point colored h. We consider a natural bilinear form on this skein module. We calculate the determinant of the matrix for this form with respect to the natural basis. We reduce the computation to count some steps in generalized Dyck paths. Moreover, we relate our determinant to a determinant on semi-meanders.",

author = "Xuanting Cai and Toufik Mansour",

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Bilinear forms on skein modules and steps in Dyck paths

Abstract

Bibliographical note

ASJC Scopus subject areas

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