The Distributions of the Entries of Young Tableaux

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...

The distributions of the entries of a Young tableau

Let T ∗ be a standard Young tableau of k cells. We show that the probability that a Young tableau of n cells contains T ∗ as a subtableau is, in the limit n → ∞, equal to ν(π(T ∗))/k!, where π(T ∗) is the shape (= Ferrers diagram) of T ∗ and ν(π) is the number of all tableaux of shape π. In other words, the probability that a large tableau contains T ∗ is equal to the number of tableaux whose s...

An Elementary Method for Computing the Kostka Coefficients

A 'Nice' Bijection for a Content Formula for Skew Semistandard Young Tableaux

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’.

Diagonal Vectors of Shifted Young Tableaux

X iv :0 80 3. 22 53 v2 [ m at h. C O ] 4 F eb 2 00 9 DIAGONAL VECTORS OF SHIFTED YOUNG TABLEAUX DORIAN CROITORU Abstra t. We study ve tors formed by entries on the diagonal of standard Young tableaux of shifted shapes. Su h ve tors are in bije tion with integer latti e points of ertain integral polytopes, whi h are Minkowski sums of simpli es. We also des ribe verti es of these polytopes, and o...