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9 papers · 2 filters
Length enumeration of fully commutative elements in finite and affine Coxeter groups
Riccardo Biagioli, Mireille Bousquet-Mélou, Frédéric Jouhet +1
An element w of a Coxeter group W is said to be fully commutative, if any reduced expression of w can be obtained from any other by transposing adjacent pairs of generators. These…
Octal Games on Graphs: The game 0.33 on subdivided stars and bistars
Laurent Beaudou, Pierre Coupechoux, Antoine Dailly +4
Octal games are a well-defined family of two-player games played on heaps of counters, in which the players remove alternately a certain number of counters from a heap, sometimes b…
Pfaffians and nonintersecting paths in graphs with cycles: Grassmann algebra methods
Sylvain Carrozza, Adrian Tanasa
After recalling the definition of Grassmann algebra and elements of Grassmann--Berezin calculus, we use the expression of Pfaffians as Grassmann integrals to generalize a series of…
Periodic Parallelogram Polyominoes
Adrien Boussicault, Patxi Laborde-Zubieta
A periodic parallelogram polyomino is a parallelogram polyomino such that we glue the first and the last column. In this work we extend a bijection between ordered trees and parall…
On the number of planar Eulerian orientations
Nicolas Bonichon, Mireille Bousquet-Mélou, Paul Dorbec +1
The number of planar Eulerian maps with n edges is well-known to have a simple expression. But what is the number of planar Eulerian orientations with n edges? This problem appears…
Strong edge-colorings of sparse graphs with large maximum degree
Ilkyoo Choi, Jaehoon Kim, Alexandr V. Kostochka +1
A {\em strong -edge-coloring} of a graph is a mapping from to such that every two adjacent edges or two edges adjacent to the same edge receive dis…