Sets of Flattened Partitions with Forbidden Patterns
Department of Mathematics
P. O. Box 7062
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.
Full version: pdf,
(Concerned with sequences
Received December 5 2020; revised version received January 1 2021.
Published in Journal of Integer Sequences,
January 2 2021.
Journal of Integer Sequences home page