Young tableaux and Arf partitions

Linked Partitions and Permutation Tableaux

Linked partitions were introduced by Dykema in the study of transforms in free probability theory, whereas permutation tableaux were introduced by Steingŕımsson and Williams in the study of totally positive Grassmannian cells. Let [n] = {1, 2, . . . , n}. Let L(n, k) denote the set of linked partitions of [n] with k blocks, let P (n, k) denote the set of permutations of [n] with k descents, and...

Skew Tableaux, Lattice Paths, and Bounded Partitions

We establish a one to one correspondence between a set of certain bounded partitions and a set of two-rowed standard Young tableaux of skew shape. Then we obtain a formula for a number which enumerates these partitions. We give two proofs for this formula, one by applying the above correspondence, the other by using the reflection principle. Finally, we give another expression for this number i...

Young tableaux

This paper gives a qualitative description how Young tableaux can be used to perform a Clebsch-Gordan decomposition of tensor products in SU(3) and how this can be generalized to SU(N).

Crystal Bases and Young Tableaux

Random Young Tableaux

We derive new combinatorial identities which may be viewed as multivariate analogs of summation formulas for hypergeometric series. As in the previous paper Re], we start with probability distributions on the space of the innnite Young tableaux. Then we calculate the probability that the entry of a random tableau at a given box equals n = 1; 2; : : :. Summing these probabilities over n and equa...