Enumeration of generalized Young tableaux with bounded height

Conjectures on the enumeration of tableaux of bounded height

Le but de cette note est essentiellement de présenter des conjectures ainsi que des indications sur les raisons qui nous ont portées à énoncer ces conjectures. Les conjectures portent sur la forme explicite d’équations de récurrence que semble satisfaire la suite th(n), des nombres de tableaux de Young de hauteur bornée par h, ainsi que la suite t (2) h (n), des nombres de paires de tels tablea...

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...

On the Enumeration of Skew Young Tableaux

Combinatorial properties of the numbers of tableaux of bounded height

Abstract. We introduce an infinite family of lower triangular matrices Γ(s), where γ (s) n,i counts the standard Young tableaux on n cells, with at most s columns, whose second and third column lengths differ by i. We show that the entries of these matrices satisfy a three-term row recurrence and we deduce recursive and asymptotic properties for the total number τs(n) of tableaux on n cells and...

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.