Ordered Partitions Avoiding a Permutation of Length 3
William Y.C. Chen, Alvin Y.L. Dai, Robin D.P. Zhou

TL;DR
This paper studies ordered partitions of a set avoiding a length-3 permutation pattern, providing generating functions and proving a conjectured recurrence relation for their enumeration.
Contribution
It derives the generating function for ordered partitions avoiding a 3-length pattern and confirms a conjecture on their recurrence relation.
Findings
Generated the explicit generating function for pattern-avoiding ordered partitions.
Proved the conjectured second order linear recurrence relation.
Extended understanding of pattern avoidance in ordered set partitions.
Abstract
An ordered partition of is a partition whose blocks are endowed with a linear order. Let be set of ordered partitions of with blocks and be set of ordered partitions in that avoid a pattern . Recently, Godbole, Goyt, Herdan and Pudwell obtained formulas for the number of ordered partitions of with 3 blocks and the number of ordered partitions of with blocks avoiding a permutation pattern of length 3. They showed that for any permutation of length 3, and raised the question concerning the enumeration of . They also conjectured that the number of ordered partitions of with blocks of size 2 avoiding a permutation pattern of length 3 satisfied a second order…
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · graph theory and CDMA systems
