Bijective enumeration of permutations starting with a longest increasing subsequence
نویسنده
چکیده
We prove a formula for the number of permutations in Sn such that their first n− k entries are increasing and their longest increasing subsequence has length n− k. This formula first appeared as a consequence of character polynomial calculations in recent work of Adriano Garsia and Alain Goupil. We give two ‘elementary’ bijective proofs of this result and of its q-analogue, one proof using the RSK correspondence and one only permutations. Résumé. Nous prouvons une formule pour le nombre des permutations dans Sn dont les prémiers n − k entrées sont croissantes et dont la plus longue sous-súite croissante est de longeur n− k. Cette formule est d’abord apparue en conséquence de calculs sur les polynômes caractères des travaux récents de Adriano Garsia et Alain Goupil. Nous donnons deux preuves bijectifs ‘élementaires’ de cet résultat et de son q-analogue, une preuve employant le corréspondance RSK et une autre n’employant que les permutations.
منابع مشابه
Enumeration of permutations starting with a longest increasing subsequence
We prove a formula for the number of permutations in Sn such that their first n−k entries are increasing and their longest increasing subsequence has length n − k. This formula first appeared as a consequence of character polynomial calculations in the work of Adriano Garsia, [2]. We give an elementary proof of this result and also of its q-analogue. In [2], Adriano Garsia derived as a conseque...
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