Open AccessCounting subword patterns in permutations arising as flattened partitions of sets
Author(s) -
Toufik Mansour,
Mark Shattuck
Publication year - 2022
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm210223009m
Subject(s) - mathematics , partition (number theory) , combinatorics , permutation (music) , flattening , context (archaeology) , set (abstract data type) , discrete mathematics , computer science , physics , materials science , acoustics , composite material , programming language , paleontology , biology
We consider various statistics on the set Fn consisting of the distinct permutations of length n+1 that arise as a flattening of some partition of the same size. In particular, we enumerate members of Fn according to the number of occurrences of three-letter consecutive patterns, considered more broadly in the context of r-partitions. As special cases of our results, we obtain formulas for the number of members of Fn avoiding a given consecutive pattern and for the total number of occurrences of a pattern over all members of Fn.