6 papers
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 Priority Lattice
Adrián Lillo, Mercedes Rosas
We introduce the priority lattice, a structure arising from the priority search algorithm on rooted trees and forests. We prove bijectively that its maximal chains are labeled by p…
On Weary Drivers, Records of Trees, and Parking Functions
Adrián Lillo, Mercedes Rosas, Stefan Trandafir
This work builds on the notion of record of rooted trees. We provide an alternative definition of parking functions, derive from it a record-preserving bijection between rooted tre…
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…
On the enumeration of records of rooted trees and rooted forests
Adrián Lillo, Mercedes Rosas, Stefan Trandafir
A record of a rooted Cayley tree is a node whose label is the largest along the unique path to the root. In this work, we find elegant functional equations relating the generating…
Non-intersecting paths and the determinant of the distance matrix of a tree
Emmanuel Briand, Luis Esquivias-Quintero, Ãlvaro Gutiérrez +2
We present the first combinatorial proof of the Graham-Pollak Formula for the determinant of the distance matrix of a tree, via sign-reversing involutions and the Lindström-Gessel…