##### This material has been published in
Discrete Math.
**139** (1995), 173-186,
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## Christian Krattenthaler and Sri Gopal Mohanty

# Counting tableaux with row and column bounds

### (12 pages)

**Abstract.**
It is well-known that the generating function for tableaux
of a given skew shape with *r* rows where the parts in the *i*'th row are
bounded
by some upper and lower bounds which depend on *i* can be written in form
of a
determinant of size *r*.
Using Gessel
and Viennot's idea of nonintersecting lattice
paths, we show that the generating function for tableaux of a given
skew shape with *r* rows and *c* columns where the parts in the *i*'th row
are bounded by upper and lower bounds which depend on *i* *and* the parts
in the *j*'th column are bounded by upper and lower bounds which
depend on *j* can also be given in determinantal form. The size of
the determinant now is *r*+2*c*.

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