A tableau inversion is a pair of entries in row-standard tableau T that lie in the same column of T yet lack the appropriate relative ordering to make T columnstandard. An i-inverted Young tableau is a row-standard tableau along with precisely i inversion pairs. Tableau inversions were originally introduced by Fresse to calculate the Betti numbers of Springer fibers in Type A, with the number o...

Abstract. The study of representations of affine Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any finite Coxeter group. This paper is completely independent of affine Hecke algebra theory and is purely combinatorial. We define generalized shapes and standard Young tableaux and show that these new objects coincide with the classi...

We give bijective proofs of pattern-avoidance results for a class of permutations generalizing alternating permutations. The bijections employed include a modified form of the RSK insertion algorithm and recursive bijections based on generating trees. As special cases, we show that the sets A2n(1234) and A2n(2143) are in bijection with standard Young tableaux of shape 〈3〉. Alternating permutati...

The study of representations of aane Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any nite Coxeter group. This paper is completely independent of aane Hecke algebra theory and is purely combinatorial. We deene generalized shapes and standard Young tableaux and show that these new objects coincide with the classical ones for root...

The purpose of this dissertation is to study certain classes of permutations and plane partitions of truncated shapes. We establish some of their enumerative and combinatorial properties. The proofs develop methods and interpretations within various fields of algebraic combinatorics, most notably the theory of symmetric functions and their combinatorial properties. The first chapter of this the...

The study of standard and generalized Young tableaux has led to interesting results in quite a number of areas of mathematics. These arrays are of importance in the representation theory of the symmetric and general linear groups [12], in invariant theory [7], and in connection with various combinatorial problems [ 11. In addition, many algorithms have been developed that manipulate the tableau...