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math.CO2026
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…
math.CO2025
Non-intersecting paths and the determinant of the distance matrix of a tree
Emmanuel Briand, Luis Esquivias-Quintero, Ãlvaro 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…