Skip to Main content Skip to Navigation
Conference papers

Periodic Patterns of Signed Shifts

Abstract : 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.
Document type :
Conference papers
Complete list of metadata

Cited literature [13 references]  Display  Hide  Download

https://hal.inria.fr/hal-01229677
Contributor : Alain Monteil Connect in order to contact the contributor
Submitted on : Tuesday, November 17, 2015 - 10:19:46 AM
Last modification on : Wednesday, June 26, 2019 - 4:36:03 PM
Long-term archiving on: : Thursday, February 18, 2016 - 11:36:19 AM

File

dmAS0174.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Kassie Archer, Sergi Elizalde. Periodic Patterns of Signed Shifts. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.873-884, ⟨10.46298/dmtcs.2350⟩. ⟨hal-01229677⟩

Share

Metrics

Record views

59

Files downloads

373