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math.CO2026
Toric Richardson Varieties and Slice Links
Thomas C. Martinez, Matthew J. Tyler
For type braid varieties, including Richardson varieties and positroid varieties, we prove that the standard torus has a dense orbit exactly when the associated link is smoothl…
math.CO2026
The Combinatorics of Affine Deodhar Diagrams
Thomas C. Martinez
Deodhar diagrams give a combinatorial way to compute point counts of open positroid varieties over finite fields. We introduce affine Deodhar diagrams, which extend this constructi…
math.CO2026
Unimodality of -Fibonomial coefficients for small cases
Brendan B. Connelly, Ezekiel Ito, Thomas C. Martinez +2
Bergeron--Ceballos--Küstner introduced the -Fibonomial coefficients \( \qfibonom{m+n}{n}\), gave a combinatorial interpretation of the -Fibonomial coefficients via a weighted…