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math.GT2026
An Extension of the Polynomial to Knotted 4-Valent Graphs
Carmen Caprau, Victoria Wiest
We use planar 4-valent graphs and a graphical calculus involving such graphs to construct an invariant for balanced-oriented, knotted 4-valent graphs. Our invariant is an extension…
math.GT2026
A whittled complex for the Khovanov homology of torus links
Carmen Caprau, Nicolle Gonzalez, Christine Ruey Shan Lee +1
We give an algorithm for reducing the number of generators of the Khovanov chain complex of the torus braid on strands by applying Bar-Na…
math.GT2024
Khovanov-Rozansky homology of Coxeter knots and Schröder polynomials for paths under any line
Carmen Caprau, Nicolle González, Matthew Hogancamp +1
We introduce a family of generalized Schröder polynomials , indexed by triangular partitions and prove that agrees with the Poincaré series of the…