VGU RESEARCH REPOSITORY
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Title: | Exhaustive generation for permutations avoiding (colored) regular sets of patterns | Authors: | Phan Thuan Do Tran Thi Thu Huong Vincent Vajnovszki |
Keywords: | Pattern avoiding permutation;Right-justified forbidden pattern;Exhaustive generating algorithm;Succession function;ECO method | Issue Date: | 2019 | Publisher: | Elsevier | Series/Report no.: | Discrete Applied Mathematics;Vol. 268 | Abstract: | Despite the fact that the field of pattern avoiding permutations has been skyrocketing over the last two decades, there are very few exhaustive generating algorithms for such classes of permutations. In this paper we introduce the notions of regular and colored regular set of forbidden patterns, which are particular cases of right-justified sets of forbidden patterns. We show the (colored) regularity of several sets of forbidden patterns (some of them involving variable length patterns) and we derive a general framework for the efficient generation of permutations avoiding them. The obtained generating algorithms are based on succession functions, a notion which is a byproduct of the ECO method introduced in the context of enumeration and random generation of combinatorial objects. For some classes of permutations falling under our general framework, the corresponding counting sequences are classical in combinatorics, such as Pell, Fibonacci, Catalan, Schröder and binomial transform of Padovan sequence. 44-53 |
Index & Ranking: | SCI (Q2) | URI(1): | http://epub.vgu.edu.vn/handle/dlibvgu/93 | DOI: | https://doi.org/10.1016/j.dam.2019.04.014 |
Appears in Collections: | ARTICLE/BOOK PUBLICATION |
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