This material has been published in
Adv. Appl. Math.
46 (2011), 144-174,
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Johann Cigler and
Some determinants of path generating functions
We evaluate four families of determinants of matrices, where the
entries are sums or differences of generating functions for paths
consisting of up-steps, down-steps and level steps. By specialisation,
these determinant evaluations have numerous corollaries. In
particular, they cover numerous determinant evaluations of
combinatorial numbers - most notably of Catalan, ballot, and of
Motzkin numbers - that appeared previously in the literature.
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