Permutations Restricted by Two Distinct Patterns of Length Three

Aaron Robertson

Permutations Restricted by Two Distinct Patterns of Length Three

Combinatorics 2007-05-23 v2

Authors: Aaron Robertson

Abstract

Define $S_n(R;T)$ to be the number of permutations on $n$ letters which avoid all patterns in the set $R$ and contain each pattern in the multiset $T$ exactly once. In this paper we enumerate $S_n(\{\alpha\};\{\beta\})$ and $S_n(\emptyset;\{\alpha,\beta\})$ for all $\alpha \neq \beta \in S_3$ . The results for $S_n(\{\alpha\};\{\beta\})$ follow from two papers by Mansour and Vainshtein.

Keywords

pattern avoidance in permutations permutations combinatorial bounds and extremal problems

Cite

@article{arxiv.math/0012029,
  title  = {Permutations Restricted by Two Distinct Patterns of Length Three},
  author = {Aaron Robertson},
  journal= {arXiv preprint arXiv:math/0012029},
  year   = {2007}
}

Comments

15 pages, some relevant reference brought to my attention (see section 4)

Permutations Restricted by Two Distinct Patterns of Length Three

Abstract

Keywords

Cite

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