337 citations · 1.3k across the 45 of their papers we have counts for
46 papers
Counting partitions by genus: a compendium of results
Robert Coquereaux, Jean-Bernard Zuber
We study the enumeration of set partitions, according to their length, number of parts, cyclic type, and genus. We introduce genus-dependent Bell, Stirling numbers, and Faà di Brun…
Counting partitions by genus. I. Genus 0 to 2
Jean-Bernard Zuber
The counting of partitions according to their genus is revisited. The case of genus 0 -- non-crossing partitions -- is well known. Our approach relies on two pillars: first a funct…
On the Minor Problem and Branching Coefficients
Jean-Bernard Zuber
The Minor problem, namely the study of the spectrum of a principal submatrix of a Hermitian matrix taken at random on its orbit under conjugation, is revisited, with emphasis on th…
On Products of Delta Distributions and Resultants
Michel Bauer, Jean-Bernard Zuber
We prove an identity in integral geometry, showing that if and are two polynomials, is proportional to where is the r…
On Schur problem and Kostka numbers
Robert Coquereaux, Jean-Bernard Zuber
We reconsider the two related problems: distribution of the diagonal elements of a Hermitian n x n matrix of known eigenvalues (Schur) and determination of multiplicities of weight…
Revisiting Horn's Problem
Robert Coquereaux, Colin McSwiggen, Jean-Bernard Zuber
We review recent progress on Horn's problem, which asks for a description of the possible eigenspectra of the sum of two matrices with known eigenvalues. After revisiting the class…