The Selberg integral and Young books ( Extended Abstract )
نویسندگان
چکیده
The Selberg integral is an important integral first evaluated by Selberg in 1944. Stanley found a combinatorial interpretation of the Selberg integral in terms of permutations. In this paper, new combinatorial objects “Young books” are introduced and shown to have a connection with the Selberg integral. This connection gives an enumeration formula for Young books. It is shown that special cases of Young books become standard Young tableaux of various shapes: shifted staircases, squares, certain skew shapes, and certain truncated shapes. As a consequence, enumeration formulas for standard Young tableaux of these shapes are obtained. Résumé. L’intégrale de Selberg est une partie intégrante importante abord évalué par Selberg en 1944. Stanley a trouvé une interprétation combinatoire de la Selberg aide en permutations. Dans ce papier, une nouvelle objets combinatoires “livre de Young” sont introduits et présentés à avoir un lien avec l’intégrale de Selberg. Cette connexion donne énumération formules pour les livres de Young. Il est démontré que spécial cas de livres de Young deviennent tableaux standards de Young de divers formes: escaliers décalées, places, certaines formes gauches et certaines formes tronquées. En conséquence, l’énumération des formules pour tableaux standards de Young de ces formes sont obtenues.
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