5 papers
A tree bijection for Eulerian orientations on quartic maps
Marie Albenque, Enrica Duchi, Juliette Schabanel
In this paper we construct a recursive bijection between -valent maps endowed with a Eulerian orientation -- also known as the ice model -- and a family of unary-binary trees. T…
Stretched exponential asymptotics for bases of triangular bootstrap percolation
Andrew Elvey Price, Juliette Schabanel, Paul Thévenin
In this paper, we study a bootstrap percolation process on the finite triangular grid of side length . We say that a subset of points in p…
Slit-Slide-Sew bijections for planar bipartite maps with prescribed degree
Juliette Schabanel
We present a bijective proof for the planar case of Louf's counting formula on bipartite planar maps with prescribed face degree, that arises from the Toda hierarchy. We actually s…
3D permutations and triangle solitaire
Juliette Schabanel
We provide a bijection between a class of 3-dimensional pattern avoiding permutations and triangle bases, special sets of integer points arising from the theory of tilings and TEP…
Solitaire of Independence
Ville Salo, Juliette Schabanel
In this paper, we study a reversible process (more precisely, a groupoid/group action) resembling the classical 15-puzzle, where the legal moves are to ``move the unique hole insid…