This project is on enumerative and algorithmic properties of partitions of integers and sets. The investigator will continue his present work on skew Young tableaux, and will pursue a new line of investigation involving q-analogs of Sterling numbers. In particular, various aspects of the Robinson-Schensted algorithm for skew tableaux will be explored, and it is hoped that various q-analogs of Stirling number identities can be given combinatorial proofs. The Robinson-Schensted algorithm gives an association between permutations of a set and pairs of standard Young tableaux of the same shape. More generally, partitions of integers and sets play an important role in combinatorics, particularly in representations of the symmetric group.
