In this paper the number of standard Young tableaux (SYT) is evaluated by the methods of multiple integrals and combinatorial summations. We obtain the product formulas of the numbers of skew SYT of certain truncated shapes, including the skew SYT ((n + k)r+1, nm−1)/(n − 1)r truncated by a rectangle or nearly a rectangle, the skew SYT of truncated shape ((n+ 1)3, nm−2)/(n− 2)\ (22), and the SYT...

This paper contains two results on the number fσ/τ of standard skew Young tableaux of shape σ/τ . The first concerns generating functions for certain classes of “periodic” shapes related to work of Gessel-Viennot and Baryshnikov-Romik. The second result gives an evaluation of the skew Schur function sλ/μ(x) at x = (1, 1/22k , 1/32k , . . . ) for k = 1, 2, 3 in terms of fσ/τ for a certain skew s...

Canonical orders, introduced in the minimal model program for orders [CI05], are simultaneous generalisations of Kleinian singularities k[[s, t]], G < SL2 and their associated skew group rings k[[s, t]]∗G. In this paper, we construct minimal resolutions of canonical orders via non-commutative cyclic covers and skew group rings. This allows us to exhibit a derived equivalence between minimal res...

A polynomial skew product of C is a map of the form f(z, w) = (p(z), q(z, w)), where p and q are polynomials, such that f extends holomorphically to an endomorphism of P of degree ≥ 2. For polynomial maps of C, hyperbolicity is equivalent to the condition that the closure of the postcritical set is disjoint from the Julia set; further, critical points either iterate to an attracting cycle or in...