Some applications of S-restricted set partitions

Abstract

In the paper, the authors present several new relations and applications for the combinatorial sequence that counts the possible partitions of a finite set with the restriction that the size of each block is contained in a given set. One of the main applications is in the study of lonesum matrices.

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Acknowledgements

The authors would like to thank the anonymous referee for some useful comments. The research of José L. Ramírez was partially supported by Universidad Nacional de Colombia, Project No. 37805.

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Correspondence to José L. Ramírez.

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Bényi, B., Ramírez, J.L. Some applications of S-restricted set partitions. Period Math Hung 78, 110–127 (2019). https://doi.org/10.1007/s10998-018-0252-1

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Keywords

  • Combinatorial identities
  • Generating functions
  • S-restricted Stirling numbers
  • Lonesum matrices
  • Poly-Bernoulli numbers

Mathematics Subject Classification

  • Primary 11B83
  • Secondary 11B73
  • 05A19
  • 05A15