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(Gould Anniversary volume) 204 (1999), 249-279,
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A New Multidimensional Matrix Inverse with applications to
We compute the inverse of a specific infinite r-dimensional matrix,
extending a matrix inverse of Krattenthaler.
Our inversion is different from the r-dimensional matrix inversion
recently found by Schlosser but generalizes a multidimensional matrix
inversion previously found by Chu. As applications of our
matrix inversion we derive some multidimensional q-series identities.
Among these are q-analogues of Carlitz' multidimensional
Abel-type expansion formulas. Furthermore, we derive a q-analogue
of MacMahon's Master Theorem.
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