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Enumeration des tableaux standards

✍ Scribed by A. Guenoche

Publisher: Elsevier Science
Year: 1979
Tongue: English
Weight: 901 KB
Volume: 25
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(79)90080-3

No coin nor oath required. For personal study only.

✦ Synopsis

Nous presentons dans cet article un aigorithme qui permet de construire parmi les tableaux standards de forme donnee (ou tableaux de Young). celui qui est de rang R. On ordonne l'ensemble des tableaux standards 51, correspondant au diagramme de Ferrers du partage a. que I'on met en bijection avec { 1,2,. . . , card 9,). L'algorithme construit, par une methode de denombrement des chemins intermediaires entre deux partages dans le treillis de Young, le R -ieme tableau.

Cette methode de rangement des tableaux standards s'applique a l'&rumCration des permutations dont les plus longues suites extraites croissantes et decroissantes sont de longueurs ;ixCes et a l'enumeration des permutations qui presentent une sequence de "croissancesdecroissances" (up-down) don&e.

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