67 citations · 203 across the 15 of their papers we have counts for
10 papers · 1 filter
Counting partial Latin rectangles and tridimensional rook placements with multisymmetric functions
Emmanuel Briand
We generalize Gessel's Formula for the number of Latin rectangles to partial Latin rectangles and non-attacking rook placements in a tridimensional chessboard. We also derive expli…
Non-intersecting paths and the determinant of the distance matrix of a tree
Emmanuel Briand, Luis Esquivias-Quintero, Álvaro Gutiérrez +2
We present the first combinatorial proof of the Graham-Pollak Formula for the determinant of the distance matrix of a tree, via sign-reversing involutions and the Lindström-Gessel-…
The 144 symmetries of the Littlewood-Richardson coefficients of
Emmanuel Briand, Mercedes Rosas
We compute with SageMath the group of all linear symmetries for the Littlewood-Richardson associated to the representations of . We find that there are 144 symmetries, more t…
On partitions with corners not containing the staircase with one more corner
Emmanuel Briand
We give three proofs of the following result conjectured by Carriegos, De Castro-Garc\'ıa and Muñoz Castañeda in their work on enumeration of control systems: when $\binom{k+1}{2}…
Normally ordered forms of powers of differential operators and their combinatorics
Emmanuel Briand, Samuel A. Lopes, Mercedes Rosas
We investigate the combinatorics of the general formulas for the powers of the operator , where is a central element of a ring and is a differential op…
Commutation and normal ordering for operators on symmetric functions
Emmanuel Briand, Peter R. W. McNamara, Rosa Orellana +1
We study the commutation relations and normal ordering between families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplic…