TL;DR
This paper derives a determinantal formula for counting meander configurations, using Gram-Schmidt orthogonalization within the Temperley-Lieb algebra, advancing combinatorial enumeration methods.
Contribution
It introduces a novel determinantal formula for meander enumeration based on algebraic orthogonalization techniques.
Findings
Derived a determinantal formula for meander counts
Connected meander enumeration to Temperley-Lieb algebra
Provided explicit orthogonalization method
Abstract
We prove a determinantal formula for quantities related to the problem of enumeration of (semi-) meanders, namely the topologically inequivalent planar configurations of non-self-intersecting loops crossing a given (half-) line through a given number of points. This is done by the explicit Gram-Schmidt orthogonalization of certain bases of subspaces of the Temperley-Lieb algebra.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Polynomial and algebraic computation