Tableaux and plane partitions of truncated shapes

Details Tableaux and plane partitions of truncated shapes Tableaux and plane partitions of truncated shapes

2010-11-03

arxiv.org/abs/1011.0795v2

Mathematics

Combinatorics

16 pages, added new formulas and sections, corrected typos, improved writing

Scientific paper

We consider a new kind of straight and shifted plane partitions/Young tableaux --- ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the number of standard tableaux in certain cases, namely a shifted staircase without the box in its upper right corner, i.e. truncated by a box, a rectangle truncated by a staircase and a rectangle truncated by a square minus a box. The proofs involve finding the generating function of the corresponding plane partitions using interpretations and formulas for sums of restricted Schur functions and their specializations. The number of standard tableaux is then found as a certain limit of this function.

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