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139 (1995), 173-186,
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Christian Krattenthaler and Sri Gopal Mohanty
Counting tableaux with row and column bounds
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
by some upper and lower bounds which depend on i can be written in form
determinant of size r.
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+2c.
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