Pattern Count on Multiply Restricted Permutations
Alina F. Y. Zhao
TL;DR
This paper investigates the enumeration of length-3 patterns in permutations with multiple restrictions, providing explicit formulas and generating functions for double and triple pattern-avoiding cases, along with combinatorial insights.
Contribution
It introduces new explicit formulas and generating functions for pattern counts in multiply restricted permutations, extending previous work on singly restricted permutations.
Findings
Derived explicit formulas for pattern occurrences
Developed generating functions for complex restrictions
Provided combinatorial interpretations for pattern relationships
Abstract
Previous work has studied the pattern count on singly restricted permutations. In this work, we focus on patterns of length 3 in multiply restricted permutations, especially for double and triple pattern-avoiding permutations. We derive explicit formulae or generating functions for various occurrences of length 3 patterns on multiply restricted permutations, as well as some combinatorial interpretations for non-trivial pattern relationships.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · semigroups and automata theory · graph theory and CDMA systems