Enumeration of Standard Young Tableaux of Shifted Strips with Constant Width

Enumeration of Standard Young Tableaux of Shifted Strips with Constant Width

Let gn1,n2 be the number of standard Young tableau of truncated shifted shape with n1 rows and n2 boxes in each row. By using the integral method this paper derives the recurrence relations of g3,n, gn,4 and gn,5 respectively. Specifically, gn,4 is the (2n− 1)-st Pell number.

Enumeration of Semi { Standard Young Tableaux

Standard tableaux. A Young tableau (also known as a standard tableau) is an arrangement of distinct integers in an array of left justiied rows, such that the entries of each row are in increasing order from left to right and the entries of each column are in increasing order from bottom to top 2. For instance, here is an array of size 15: 11 4 8 12 14 3 6 7 13 1 2 5 9 10 15 : In general a table...

Enumeration of Standard Young Tableaux of certain Truncated Shapes

Unexpected product formulas for the number of standard Young tableaux of certain truncated shapes are found and proved. These include shifted staircase shapes minus a square in the NE corner, rectangular shapes minus a square in the NE corner, and some variations.

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 o...

On the Enumeration of Skew Young Tableaux