On the effective and automatic enumeration of polynomial permutation classes. (September 2016)

• Record Type: Journal Article
• Authors: Homberger, Cheyne; Vatter, Vincent
• Is Part Of: Journal of symbolic computation. Volume 76(2016)
• Page Start: 84
• Page End: 96
• Publication Date: 2016-09
• Subjects: primary 05A15 -- secondary 05A05; Permutation patterns -- Polynomial class -- Rational generating function; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.11.019
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations of length n which can be obtained by a finite number of block sorting operations (e.g., reversals, block transpositions, cut-and-paste moves).