234 research outputs found
Poly-Bernoulli numbers and lonesum matrices
A lonesum matrix is a matrix that can be uniquely reconstructed from its row
and column sums. Kaneko defined the poly-Bernoulli numbers by a
generating function, and Brewbaker computed the number of binary lonesum
-matrices and showed that this number coincides with the
poly-Bernoulli number . We compute the number of -ary lonesum
-matrices, and then provide generalized Kaneko's formulas by using
the generating function for the number of -ary lonesum -matrices.
In addition, we define two types of -ary lonesum matrices that are composed
of strong and weak lonesum matrices, and suggest further researches on lonesum
matrices. \Comment: 27 page
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