Pattern avoidance of -pairs in circular permutations
arXiv:2111.04925 · doi:10.1016/j.aam.2022.102346
Abstract
The study of pattern avoidance in linear permutations has been an active area of research for almost half a century now, starting with the work of Knuth in 1973. More recently, the question of pattern avoidance in circular permutations has gained significant attention. In 2002-03, Callan and Vella independently characterized circular permutations avoiding a single permutation of size . Building on their results, Domagalski et al. studied circular pattern avoidance for multiple patterns of size . In this article, our main aim is to study circular pattern avoidance of -pairs, i.e., circular permutations avoiding one pattern of size 4 and another of size . We do this by using well-studied combinatorial objects to represent circular permutations avoiding a single pattern of size . In particular, we obtain upper bounds for the number of Wilf equivalence classes of -pairs. Moreover, we prove that the obtained bound is tight when the pattern of size in consideration is . Using ideas from our general results, we also obtain a complete characterization of the avoidance classes for -pairs.
First section split into two; other minor changes; final version