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- W1966341782 abstract "Carlitz, Handa, and Mohanty proved determinantal formulas for counting partitions contained in a fixed bounding shape by area. Gessel and Viennot introduced a combinatorial method for proving such formulas by interpreting the determinants as counting suitable configurations of signed lattice paths. This note describes an alternative combinatorial approach that uses sign-reversing involutions to prove matrix inversion results. Combining these results with the classical adjoint formula for the inverse of a matrix, we obtain a new derivation of the Handa–Mohanty determinantal formula." @default.
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- W1966341782 date "2010-01-01" @default.
- W1966341782 modified "2023-10-16" @default.
- W1966341782 title "Note on enumeration of partitions contained in a given shape" @default.
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- W1966341782 doi "https://doi.org/10.1016/j.laa.2009.09.006" @default.
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