Equivariant Euler characteristics on permutohedral varieties

Vincenzo Galgano; Hanieh Keneshlou; Mateusz Michalek

doi:10.1007/978-981-97-3886-1_7

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arXiv · 2302.04598

Equivariant Euler characteristics on permutohedral varieties

Vincenzo Galgano·Hanieh Keneshlou·Mateusz Michalek

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Abstract

By the work of J.Huh, one can interpret binomial coefficients as a solution to an intersection problem on a permutohedral variety $X_E$. Applying Hirzebruch-Riemann-Roch, this intersection problem is equivalent to computing Euler characteristic of a specific element of $K$-theory of $X_E$. This element has a natural lifting to equivariant $K$-theory and thus the Euler characteristic may be upgraded to a Laurent polynomial. We provide and implement three different approaches, in particular a recursive one, to computing these polynomials.

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Vincenzo Galgano, Hanieh Keneshlou, Mateusz Michalek. 2023-02-09. Equivariant Euler characteristics on permutohedral varieties. https://doi.org/10.1007/978-981-97-3886-1_7

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