Bijections between oscillating tableaux and (semi)standard
tableaux via growth diagrams
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
is equal to the number of standard Young tableaux of size n
with m columns of odd length, all columns of length
at most 2k. 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.
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