Creation of ballot sequences in a periodic cellular automaton
| dc.creator | Takagi, Taichiro | |
| dc.date | 2007-08-06 | |
| dc.date | 2009-02-10 | |
| dc.date.accessioned | 2026-07-07T12:39:01Z | |
| dc.date.available | 2026-07-07T12:39:01Z | |
| dc.description | Motivated by an attempt to develop a method for solving initial value problems in a class of one dimensional periodic cellular automata (CA) associated with crystal bases and soliton equations, we consider a generalization of a simple proposition in elementary mathematics. The original proposition says that any sequence of letters 1 and 2, having no less 1's than 2's, can be changed into a ballot sequence via cyclic shifts only. We generalize it to treat sequences of cells of common capacity s > 1, each of them containing consecutive 2's (left) and 1's (right), and show that these sequences can be changed into a ballot sequence via two manipulations, cyclic and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various kink-like structures are traveling along the system like particles under the time evolution of this rule. | |
| dc.description | 31 pages. Section 1 changed and section 5 added | |
| dc.identifier | https://arxiv.org/abs/0708.0705 | |
| dc.identifier | http://arxiv.org/abs/0708.0705 | |
| dc.identifier | J. Phys. Soc. Jpn. 78 (2009) 024003 | |
| dc.identifier | doi:10.1143/JPSJ.78.024003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218965 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | Combinatorics | |
| dc.title | Creation of ballot sequences in a periodic cellular automaton | |
| dc.type | text |