Diagonal Vectors of Shifted Young Tableaux

X iv :0 80 3. 22 53 v2 [ m at h. C O ] 4 F eb 2 00 9 DIAGONAL VECTORS OF SHIFTED YOUNG TABLEAUX DORIAN CROITORU Abstra t. We study ve tors formed by entries on the diagonal of standard Young tableaux of shifted shapes. Su h ve tors are in bije tion with integer latti e points of ertain integral polytopes, whi h are Minkowski sums of simpli es. We also des ribe verti es of these polytopes, and onstru t orresponding shifted Young tableaux. 1. Shifted Young Diagrams And Tableax De nition 1. Let λ = (λ1, . . . , λn) be a partition with at most n parts. The shifted Young diagram of shape λ (or just λ-shifted diagram) is the set Dλ = { (i, j) ∈ R| 1 ≤ j ≤ n, j ≤ i ≤ n+ λj }