An Analog of Schensted's Algorithm for Shifted Young Tableaux

For example “i” is a YT of shape (4, 3, 1). The YT is said to be standard (an SYT) if the integers in the tableau are 1, 2,..., n as in “. A partition p = (pl, p2 ,..., pt) is strict if p1 > t+ > ... > pt > 0. A generalized Shzyted Young Tableau (abbreviated ST) of shape p is an array of n-integers into t rows with row i containing pi integers and indented i 1 spaces, such that the rows are non-decreasing and the columns are strictly increasing. The ST is said to be standard (an SST) if the integers in the tableau are 1, 2,..., n. The diagonal of an ST is the set of first elements in each row. All other elements of the ST are off-diagonal. In the SST ‘2 the diagonal is { 1, 3). Schensted’s algorithm [3] establishes a one-to-one correspondence between permutations of the integers 1, 2,..., n and pairs of SYT of the same shape having n entries. For this bijection we write 7~ t) (P(r), Q(T)) where P(n) and Q(r) are called the P and Q shapes of r respectively. An immediate corollary of this correspondence is the formula