eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2010-01-01
Vol. 12 no. 2
10.46298/dmtcs.517
517
journal article
Tiling Periodicity
Juhani Karhumaki
Yury Lifshits
Wojciech Rytter
We contribute to combinatorics and algorithmics of words by introducing new types of periodicities in words. A tiling period of a word w is partial word u such that w can be decomposed into several disjoint parallel copies of u, e.g. a lozenge b is a tiling period of a a b b. We investigate properties of tiling periodicities and design an algorithm working in O(n log (n) log log (n)) time which finds a tiling period of minimal size, the number of such minimal periods and their compact representation. The combinatorics of tiling periods differs significantly from that for classical full periods, for example unlike the classical case the same word can have many different primitive tiling periods. We consider also a related new type of periods called in the paper multi-periods. As a side product of the paper we solve an open problem posted by T. Harju (2003).
https://dmtcs.episciences.org/517/pdf
algorithms on word
periodicities
tilers
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]