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math.CO2026
Positive expansions of permuted basement and quasisymmetric Macdonald polynomials at
Olya Mandelshtam, Harper Niergarth, Kartik Singh
It is well known that the -Whittaker polynomials, which are specializations of the Macdonald polynomials , expand positively as the sum of Schur polynomials. M…
math.CO2025
Parametrizing the Grassmannian using pipe dreams
Kartik Singh
Postnikov gave a parametrization for the totally non-negative Grassmannian using the matroid decomposition and associating a network with \reflectbox{L}-diagrams. Talaska and Willi…
math.CO2022
Identities of the multi-variate independence polynomials from heaps theory
Deniz Kus, Kartik Singh, R. Venkatesh
We study and derive identities for the multi-variate independence polynomials from the perspective of heaps theory. Using the inversion formula and the combinatorics of partially c…