Abstract numeration systems on bounded languages and multiplication by a constant
| dc.creator | Charlier, Emilie | |
| dc.creator | Rigo, Michel | |
| dc.creator | Steiner, Wolfgang | |
| dc.date | 2007-06-04 | |
| dc.date | 2008-09-16 | |
| dc.date.accessioned | 2026-07-07T10:02:37Z | |
| dc.date.available | 2026-07-07T10:02:37Z | |
| dc.description | A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems built over bounded languages with at least three letters, we show that multiplication by an integer $λ\ge2$ does not preserve $S$-recognizability, meaning that there always exists a $S$-recognizable set $X$ such that $λX$ is not $S$-recognizable. The main tool is a bijection between the representation of an integer over a bounded language and its decomposition as a sum of binomial coefficients with certain properties, the so-called combinatorial numeration system. | |
| dc.identifier | https://arxiv.org/abs/0706.0431 | |
| dc.identifier | http://arxiv.org/abs/0706.0431 | |
| dc.identifier | Integers: Electronic Journal of Combinatorial Number Theory 8, 1 (2008) #35 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169037 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Combinatorics | |
| dc.title | Abstract numeration systems on bounded languages and multiplication by a constant | |
| dc.type | text |