Abstract
The Bn(k) poly-Bernoulli numbers — a natural generalization of classical Bernoulli numbers (Bn = Bn(1)) — were introduced by Kaneko in 1997. When the parameter k is negative then Bn(k) is a nonnegative number. Brewbaker was the first to give combinatorial interpretation of these numbers. He proved that Bn(−k) counts the so called lonesum 0–1 matrices of size n × k. Several other interpretations were pointed out. We survey these and give new ones. Our new interpretation, for example, gives a transparent, combinatorial explanation of Kaneko’s recursive formula for poly-Bernoulli numbers.
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