3 papers
math.CO2026
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…
math.CO2026
A construction of the hat tilings by a Markov partition
Sébastien Labbé, Peter Selinger
We present a simple construction of hat tilings. The construction can be carried out by superimposing a triangular grid on a specially colored image and reading off the orientation…
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…