Macdonald polynomials and operators and Catalan Combinatorics
Fran\c{c}ois Bergeron
TL;DR
This paper introduces combinatorial and symmetric function tools to describe the Poincare polynomial of triply graded Khovanov-Rozansky homology of torus links, connecting algebraic invariants with combinatorial structures.
Contribution
It develops new combinatorial and symmetric function methods to analyze the superpolynomial of torus links, bridging knot homology and algebraic combinatorics.
Findings
New tools for computing the superpolynomial of torus links
Connections established between symmetric functions and link invariants
Enhanced understanding of the algebraic structure of link homologies
Abstract
Our main aim with these notes is to introduce the combinatorial and symmetric function tools that relate to the description of the Poincare polynomial of the triply graded Khovanov-Rozansky homology of torus links, a.k.a. the (reduced) superpolynomial of these links.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology