The University of Michigan Combinatorics Seminar


Abstract 

The skew LittlewoodRichardson 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 LR 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 LR 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 LR 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 dcomplete poset is
simultaneous and hence jdt.)
