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Extending Fine sequences: a link with forbidden patterns

Olivier Guibert·Sylvain Pelat-Alloin
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Abstract

We propose a natural, bivariate, generalization of the nonsingular similarity relations considered by T. Fine. We also provide an enumeration formulae and a generating tree for those relations. The latter allow us to give a new bijection between 321-avoiding derangements and Fine sequences. Moreover, we establish that two special cases are in a one-to-one correspondence with subsets of permutations characterized by forbidden subsequences on the symmetrical group. All our results are established using the technique of generating tree, thus giving entirely bijective proofs.

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Olivier Guibert, Sylvain Pelat-Alloin. 2005-07-20. Extending Fine sequences: a link with forbidden patterns. https://arxiv.org/abs/math/0507408

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