## Christian Krattenthaler

# Bijections between oscillating tableaux and (semi)standard
tableaux via growth diagrams

### (29 pages)

**Abstract.**
We prove that
the number of oscillating tableaux
of length *n* with at most *k* columns,
starting at the empty partition and ending at the one-column shape
(1*m*),
is equal to the number of standard Young tableaux of size *n*
with *m* columns of odd length, all columns of length
at most 2*k*. This refines a conjecture of Burrill,
which it thereby establishes.
We prove as well a "Knuth-type" extension stating a similar
equi-enumeration result between generalised oscillating tableaux
and semistandard tableaux.

The following versions are available:

Back to Christian Krattenthaler's
home page.