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Forest-Like Permutations

By: Mireille Bousquet-Mélou; Steve Butler;

2008 / Springer Science+Business Media / 0218-0006

Description

Given a permutation is a forest. We first characterize forest-like permutations in terms of pattern avoidance, and then by a certain linear map being onto. Thanks to recent results of Woo and Yong, these show that forest-like permutations characterize Schubert varieties which are locally factorial. Thus forest-like permutations generalize smooth permutations (corresponding to smooth Schubert varieties). We compute the generating function of forest-like permutations. As in the smooth case, it turns out to be algebraic. We then adapt our method to count permutations for which is a tree, or a path, and recover the known generating function of smooth permutations.