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The Varchenko Matrix for Dehyperplane Arrangement
Hery Randriamaro
This article computes the Varchenko determinant of dehyperplane arrangements which are generalizations of pseudohyperplane arrangements. But unlike those latter, they are defined o…
Diagonalization of Fix-Mahonian Matrices
Hery Randriamaro
Consider the regular representation of the sum over all permutations weighted by the sum of their descent, inversion, and fixed point multinomials. We compute the spectrum and the…
Face Counting for Topological Hyperplane Arrangements
Hery Randriamaro
Determining the number of pieces after cutting a cake is a classical problem. Roberts (1887) provided an exact solution by computing the number of chambers contained in a plane cut…
The Varchenko Determinant of an Oriented Matroid
Hery Randriamaro
Varchenko introduced in 1993 a distance function on the chambers of a hyperplane arrangement that gave rise to a determinant whose entry in position is the distance betwee…