%0 Journal Article
%T Dyck Paths, Standard Young Tableaux, and Pattern Avoiding Permutations
%A Hilmar Gudmundsson
%J Mathematics
%D 2009
%I arXiv
%X We present a generating function and a closed counting formula in two variables that enumerate a family of classes of permutations that avoid or contain an increasing pattern of length three and have a prescribed number of occurrences of another pattern of length three. This gives a refinement of some previously studied statistics, most notably one by Noonan. The formula is also shown to enumerate a family of classes of Dyck paths and Standard Young Tableaux, and a bijection is given between the corresponding classes of these two families of objects. Finally, the results obtained are used to solve an optimization problem for a certain card game.
%U http://arxiv.org/abs/0912.4747v1