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The Selberg integral and Young books
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.Comment: 13 pages, 11 figure
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