Bilinear forms on skein modules and steps in Dyck paths

Xuanting Cai, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number073509
JournalJournal of Mathematical Physics
Issue number7
StatePublished - 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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