3 papers
math.CO2026
Middle orders: all distributive lattices between weak and Bruhat
Ludovic Schwob
For a given Coxeter group, we study distributive lattices called middle orders refining the weak order and refined by the Bruhat order. In type , we construct such lattices inde…
math.CO2026
Heaps of rhombic dodecahedra, catalan congruences on alternating sign matrices, and bases of the Temperley-Lieb algebra
Florent Hivert, Vincent Pilaud, Ludovic Schwob
We prove that the excedance relation on permutations defined by N. Bergeron and L. Gagnon actually extends to a congruence of the lattice on alternating sign matrices. Motivated by…
math.CO2025
On the enumeration of double cosets and self-inverse double cosets
Ludovic Schwob
Double cosets appear in many contexts in combinatorics, for example in the enumeration of certain objects up to symmetries. Double cosets in a quotient of the form $H\backslash G /…