The (shifted) plactic monoid. The celebrated Robinson-Schensted-Knuth correspondence (14) is a bijection between words in a linearly ordered alphabet X = {1 < 2 < 3 < · · · } and pairs of Young tableaux with entries in X . More precisely, each word corresponds to a pair consisting of a semistandard insertion tableau and a standard recording tableau. The words producing a given insertion tableau...

Bijective proofs of the hook formulas for the number of ordinary standard Young tableaux and for the number of shifted standard Young tableaux are given. They are formulated in a uniform manner, and in fact prove q-analogues of the ordinary and shifted hook formulas. The proofs proceed by combining the ordinary, respectively shifted, Hillman–Grassl algorithm and Stanley's (P, ω)-partition theor...

Richardson varieties are obtained as intersections of Schubert and opposite varieties. We provide a new family toric degenerations inside Grassmannians by studying Gröbner their corresponding ideals. These parametrised block diagonal matching fields in the sense Sturmfels [33]. associate weight vector to each field study its initial ideal. In particular, we characterise when such ideals toric, ...

Based on Schützenberger’s evacuation and a modification of jeu de taquin, we give a bijective proof of an identity connecting the generating function of reverse semistandard Young tableaux with bounded entries with the generating function of all semistandard Young tableaux. This solves Exercise 7.102 b of Richard Stanley’s book ‘Enumerative Combinatorics 2’.

The RSK correspondence generalises the Robinson-Schensted correspondence by replacing permutation matrices by matrices with entries in N, and standard Young tableaux by semistandard ones. For r ∈ N>0, the Robinson-Schensted correspondence can be trivially extended, using the r-quotient map, to one between r-coloured permutations and pairs of standard r-ribbon tableaux built on a fixed r-core (t...

Recent works in algebraic combinatorics have brought up to date the importance of certain planar structures, called ribbon tableaux, which are generalizations of Young tableaux. This paper gives an algorithm to eeciently distribute, using PVM, the computation of the set of all ribbon tableaux of given shape and weight. It also provides a way to compute the spin polynomials associated to those s...

We develop two combinatorial proofs of the fact that certain Young tableaux are counted by the Catalan numbers. The setting is a larger class of tableaux where labels increase along rows without attention to whether labels increase down columns. We define a new operation called tableau cycling. It is used to duplicate the reflection argument attributed to André in the tableaux setting, and also...