4 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, als…