The Selberg integral and Young books

详细信息    查看全文

• 作者：Jang Soo Kim^a ; ¹ ; ^{jangsookim@skku.edu" class="auth_mail" title="E-mail the corresponding author} ; Suho Oh^b ; ^{suhooh@txstate.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Selberg integral ; Standard Young tableau ; Product formula ; Truncated shape
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：145
• 期：Complete
• 页码：1-24
• 全文大小：586 K

文摘

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, product formulas for the number of standard Young tableaux of these shapes are obtained.