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In [4], Gurevich, Pyatov and Saponov stated an expansion for the product of two Schur functions and gave a proof based on the Plücker relations. Here we show that this identity is in fact a special case of a quite general Schur function identity, which was stated and proved in [1, Lemma 16]. In [1], it was used to prove bijectively Dodgson's condensation(More)
We give bijective proofs for Jacobi{Trudi-type and Giambelli-type identities for symplectic and orthogonal characters. These proofs base on interpreting King and El-Sharkaway's symplectic tableaux, Proctor's odd and intermediate symplectic tableaux, Proctor's and King and Welsh's orthogonal tableaux, and Sundaram's odd orthogonal tableaux in terms of(More)
We consider the problem of enumerating the permutations containing exactly k occurrences of a pattern of length 3. This enumeration has received a lot of interest recently, and there are a lot of known results. This paper presents an alternative approach to the problem, which yields a proof for a formula which so far only was conjectured (by Noonan and(More)
We compute the number of rhombus tilings of a hexagon with side lengths having the same parity, which contain a particular rhombus next to the center of the hexagon. The special case N = M of one of our results solves a problem posed by Propp. In the proofs, Hankel determinants featuring Bernoulli numbers play an important role. 1. Introduction Let a, b and(More)
The purpose of this note is to exhibit clearly how the " graphical condensation " identities of Kuo, Yan, Yeh and Zhang follow from classical Pfaffian identities by the Kasteleyn–Percus method for the enumeration of matchings. Knuth termed the relevant identities " overlapping Pfaffian " identities and the key concept of proof " su-perpositions of matchings(More)
We show how a formula concerning " vicious walkers " (which basically are nonintersecting lattice paths) on the cylinder given by P.J. Forrester can be proved and generalized by using the Lindström–Gessel–Viennot method, after having things set up in the right way. We apply the corresponding results to the (thermodynamic limit of the) free energy of the "(More)