Abstract
In this paper we consider the enumeration of three kinds of standard Young tableaux (SYT) of truncated shapes by use of the method of multiple integrals. A product formula for the number of truncated shapes of the form (nm, n − r)\\δk–1 is given, which implies that the number of SYT of truncated shape (n2, 1)\\(1) is the number of level steps in all 2-Motzkin paths. The number of SYT with three rows truncated by some boxes ((n + k)3)\\(k) is discussed. Furthermore, the integral representation of the number of SYT of truncated shape (nm)\\(3, 2) is derived, which implies a simple formula of the number of SYT of truncated shape (nn)\\(3, 2).
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