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math.CO2026
Real-rooted Eulerian polynomials from permutations, words, and paths
Per Alexandersson
We study six Eulerian-type polynomial families. We prove that the descent polynomials of derangements are real-rooted, settling the derangement part of a conjecture of S.~Fu, Z.~Li…
math.CO2026
Fast computation of Ehrhart polynomials of Gelfand--Tsetlin polytopes via Macdonald reciprocity
Per Alexandersson
We describe an efficient method for computing the Ehrhart polynomial of Gelfand--Tsetlin polytopes arising from Kostka coefficients. The key idea is to exploit Ehrhart--Macdonald r…
math.CO2026
Polynomials from tilings of rectangles
John Ahlberg, Per Alexandersson
We study tilings of rectangular boards using unit squares together with a single type of big tile shaped as a Ferrers diagram. We derive generating functions for these tilings, pro…