DOAJ
Open Access
2013
Periodic Patterns of Signed Shifts
Kassie Archer
Sergi Elizalde
Abstrak
The periodic patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial description of the periodic patterns of an arbitrary signed shift, in terms of the structure of the descent set of a certain transformation of the pattern. Signed shifts are an important family of one-dimensional dynamical systems. For particular types of signed shifts, namely shift maps, reverse shift maps, and the tent map, we give exact enumeration formulas for their periodic patterns. As a byproduct of our work, we recover some results of Gessel and Reutenauer and obtain new results on the enumeration of pattern-avoiding cycles.
Topik & Kata Kunci
Penulis (2)
K
Kassie Archer
S
Sergi Elizalde
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2013
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2350
- Akses
- Open Access ✓