The University of Michigan Combinatorics Seminar
Winter 2003
April 11, 4:10-5:00, 3866 East Hall





Jeu de Taquin Posets and the Littlewood-Richardson Rule

Robert Proctor

University of North Carolina, Chapel Hill




Abstract

The skew Littlewood-Richardson rule expresses a skew Schur function as a certain sum of Schur functions. If (skew) Schur functions are viewed as sets of semistandard Young tableaux, then the L-R rule can be pictured in terms of "shoving" the entries of the given skew tableaux to the northwest to form ordinary tableaux. This talk will present a minimalist version of such a bijective proof of the L-R rule which does not refer to Knuth relations or to Schensted's correspondence, and which refers to rows and columns as little and as late as possible. The earliest and most fundamental part of the proof can be generalized to any poset which possesses a well defined jeu de taquin emptying procedure, and it is conjectured that any poset which possesses such L-R decompositions must conversely possess the jeu de taquin property. Time permitting, the simultaneous property (which is stronger than the jdt property) will be defined for posets. (It is known that every d-complete poset is simultaneous and hence jdt.)