Extending Fine sequences: a link with forbidden patterns
英文摘要：
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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