Journal of Integer Sequences, Vol. 24 (2021), Article 21.1.5

Sets of Flattened Partitions with Forbidden Patterns

Olivia Nabawanda
Department of Mathematics
Makerere University
P. O. Box 7062

Fanja Rakotondrajao
Département de Mathématiques et Informatique
Université d'Antananarivo, Antananarivo


The study of pattern avoidance in permutations, and specifically in flattened partitions is an active area of current research. In this paper, we count the number of distinct flattened partitions over [n] avoiding a single pattern, as well as a pair of two patterns. Several counting sequences, namely Catalan numbers, powers of two, Fibonacci numbers and Motzkin numbers arise. We also consider other combinatorial statistics, namely runs and inversions, and establish some bijections in situations where the statistics coincide.

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(Concerned with sequences A000012 A000045 A000108 A001006 A011782 A028310.)

Received December 5 2020; revised version received January 1 2021. Published in Journal of Integer Sequences, January 2 2021.

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