Speaker: Michael Shynar (Bar-Ilan University)

Title: "On Inversions in Standard Young Tableaux"

Abstract:
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Formulation of the Robinson-Schensted algorithm (connecting permutations
and standard Young tableaux) and extensive studies of it, led to the
recognition that certain statistics (primarily: the descent number) on
permutations and on standard Young tableaux, are closely related. However,
no such results exist for the inversion number. This work introduces the
inversion number on standard Young tableaux and determines their
distribution over hook-shaped tableaux. We also define the sign of a
tableaux and determine its distribution over $(n-k,k)$-shaped tableaux.
The results seem closely related to results achieved in the field of
pattern-avoiding permutations by Adin, Roichman and Reifegerste.