Weighted lonesum matrices and their generating function. (English) Zbl 1283.15046
Summary: A lonesum matrix is a \((0, 1)\)-matrix uniquely determined by its column and row sums, and the sum of its all entries is called the “weight” of it. The generating function of numbers of weighted lonesum matrices of each weight is given. A certain explicit formula for the number of weighted lonesum matrices is also proved.
MSC:
| 15A24 | Matrix equations and identities |
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 11G55 | Polylogarithms and relations with \(K\)-theory |
