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math.CO2025
-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…
math.CO2025
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…
math.CO2025
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…