2006/03/20 by Adam M. Goyt, Goyt, Adam M. · 2 citations
Engineering · Mathematics · #05A15 #05A18 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.math/0603481
openalex publication_date 2006/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Klazar defined and studied a notion of pattern avoidance for set partitions, which is an analogue of pattern avoidance for permutations. Sagan considered partitions which avoid a single partition of three elements. We enumerate partitions which avoid any family of partitions of a 3-element set as was done by Simion and Schmidt for permutations. We also consider even and odd set partitions. We provide enumerative results for set partitions restricted by generalized set partition patterns, which are an analogue of the generalized permutation patterns of Babson and Steingr'ımsson. Finally, in the spirit of work done by Babson and Steingr'ımsson, we will show how these generalized partition patterns can be used to describe set partition statistics.