Reconstructing Young tableaux

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).

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...

Inversions of Semistandard Young Tableaux

A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau columnstandard. An i-inverted Young tableau is a row-standard tableau with precisely i inversion pairs, and may be interpreted as a generalization of (column-standard) Young tableaux. Inverted Young tableaux that lack repeated entries were introdu...

Crystal Bases and Young Tableaux

Pattern Avoidance and Young Tableaux

Motivated by [13, Theorem 4.1], this paper extends Lewis’s bijection to a bijection between a more general class L(n, k, I) of permutations and the set of standard Young tableaux of shape 〈(k + 1)n〉, so the cardinality |L(n, k, I)| = f 〈(k+1)n〉, is independent of the choice of I ⊆ [n]. As a consequence, we obtain some new combinatorial realizations and identities on Catalan numbers. In the end,...