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  • 1 József Eötvös College, Bajcsy-Zsilinszky u. 14., Baja 6500, Hungary
  • 2 University of Szeged, Aradi Vértanúk tere 1., Szeged 6720, Hungary
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The Bn (k) poly-Bernoulli numbers — a natural generalization of classical Bernoulli numbers (B n = 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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