3 papers
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…
math.AC2025
Equations, inequations and inequalities characterizing the configurations of two real projective conics
Emmanuel Briand
Ordered pairs of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and ineq…