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A Generalization of the Gram determinant of type A

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arxiv 1905.07834 v1 pith:7GVNVMBZ submitted 2019-05-20 math.GT math.CO

Rhea Palak Bakshi , Dionne Ibarra , Sujoy Mukherjee , Józef H. Przytycki This is my paper · ORCID
classification math.GTmath.CO
keywords determinantgramtypeannulusbilinearbottlechenclosed
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abstract

The Gram determinant of type $A$ was introduced by Lickorish in his work on invariants of 3 - manifolds. We generalize the theory of the Gram determinant of type $A$ by evaluating, in the annulus, a bilinear form of non-intersecting connections in the disc. The main result provides a closed formula for this Gram determinant. We conclude the paper by discussing Chen's conjecture about the Gram determinant of type $Mb$ evaluated in the Klein bottle.

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  1. Chebyshev polynomials and Gram determinants from the M\"obius band

    math.GT 2025-04 reject novelty 5.0 of 10

    The paper proves that the (2^k-1)th second-kind Chebyshev polynomial factors as a product of first-kind Chebyshev polynomials, restates two Gram determinant conjectures, and proves a supporting divisibility factor tha...

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