Equivariant Euler characteristics on permutohedral varieties

2023/02/09 by Vincenzo Galgano, Galgano, Vincenzo, Hanieh Keneshlou +3
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2302.04598

openalex publication_date 2023/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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