0

Standard tableaux. A Young tableau (also known as a standard tableau) is an arrangement of distinct integers in an array of left justiied rows, such that the entries of each row are in increasing order from left to right and the entries of each column are in increasing order from bottom to top 2. For instance, here is an array of size 15: 11 4 8 12 14 3 6 7 13 1 2 5 9 10 15 : In general a table...

Young’s lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young...

We present families of tableaux which interpolate between the classical semi-standard Young and matching field tableaux. Algebraically, this corresponds to SAGBI bases Plücker algebras . show that each such family leads a toric ideal, can be realized as initial hence degeneration for flag variety.

Abstract In this note, we provide a short proof of Theorem 4.3 in the paper titled Crystals, semistandard tableaux and cyclic sieving phenomenon , by Y.-T. Oh E. Park, which concerns on semi-standard Young tableaux. We also extend their result to skew shapes.

The number of words w = w 1 w n , 1 w i k, standard and semi-standard Young tableaux. When n ! 1, the asymptotics of the number of such words is calculated.

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...

For any polynomial representation of the special linear group, the nodes of the corresponding crystal may be indexed by semi-standard Young tableaux. Under certain conditions, the standard Young tableaux occur, and do so with weight 0. Standard Young tableaux also parametrize the vertices of dual equivalence graphs. Motivated by the underlying representation theory, in this paper, we explain th...