11 citations · 32 across the 12 of their papers we have counts for
12 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…
The Genesis Sequence, Tree Records and Endofunctions
Enrica Duchi, Adrián Lillo, Pablo Puerto +2
We present bijections connecting tree records, the girth of a connected endofunction, and the genesis sequence (the first sequence in OEIS). Using these, we derive generating funct…
The genesis sequence, tree records and endofunctions
Enrica Duchi, Adrián Lillo, Pablo Puerto +2
In this work, we present a series of bijections that reveal the deep connections between the concepts of tree records, the girth of a connected endofunction, and the genesis sequen…
From order one catalytic decompositions to context-free specifications: the rewiring bijection
Enrica Duchi, Gilles Schaeffer
A celebrated result of Bousquet-Mélou and Jehanne states that the bivariate power series solutions of so-called combinatorial polynomial equations with one catalytic variable, also…
A bijection between rooted planar maps and generalized fighting fish
Enrica Duchi, Corentin Henriet
The class of fighting fish is a recently introduced model of branching surfaces generalizing parallelogram polyominoes. We can alternatively see them as gluings of cells, walks on…
A bijection between Tamari intervals and extended fighting fish
Enrica Duchi, Corentin Henriet
We introduce extended fighting fish as branching surfaces that can also be seen as walks in the quarter plane defined by simple rewriting rules. The main result we present in the a…