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112 papers · 1 filter
-analogs of rational numbers: from Ostrowski numeration systems to perfect matchings
Jean-Christophe Aval, Sébastien Labbé
We consider the -deformation of rational numbers introduced recently by Morier-Genoud and Ovsienko. We propose three enumerative interpretations of these -rationals: in terms…
When Many Trees Go to War: On Sets of Phylogenetic Trees With Almost No Common Structure
Mathias Weller, Norbert Zeh
It is known that any two trees on the same leaves can be displayed by a network with reticulations, and there are two trees that cannot be displayed by a network with few…
Positionality of Dumont--Thomas numeration systems for integers
Savinien Kreczman, Sébastien Labbé, Manon Stipulanti
Introduced in 2001 by Lecomte and Rigo, abstract numeration systems provide a way of expressing natural numbers with words from a language accepted by a finite automaton. As it…
Partitions of planar (oriented) graphs into a connected acyclic and an independent set
Stijn Cambie, François Dross, Kolja Knauer +2
A question at the intersection of Barnette's Hamiltonicity and Neumann-Lara's dicoloring conjecture is: Can every Eulerian oriented planar graph be vertex-partitioned into two acyc…
A Galois structure on the orbit of large steps walks in the quadrant
Pierre Bonnet, Charlotte Hardouin
The enumeration of weighted walks in the quarter plane reduces to studying a functional equation with two catalytic variables. When the steps of the walk are small, Bousquet-Mélou…
Constructing disjoint Steiner trees in Sierpiński graphs
Chenxu Yang, Ping Li, Yaping Mao +2
Let be a graph and with . Then the trees in are \emph{internally disjoint Steiner trees} connecting (or -Stei…