Distinct Parts Partitions without Sequences

  • Kathrin Bringmann
  • Karl Mahlburg
  • Karthik Nataraj
Keywords: Rogers-Ramanujan, integer partitions, distinct parts


Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties, hypergeometric representations for the generating functions, and asymptotic formulas for the enumeration functions. We complete a similar investigation of partitions into distinct parts without sequences, which are of particular interest due to their relationship with the Rogers-Ramanujan identities. Our main results include a double series representation for the generating function, an asymptotic formula for the enumeration function, and several combinatorial inequalities.

Author Biographies

Kathrin Bringmann, University of Cologne

Department of Mathematics

Karl Mahlburg, Louisiana State University
Department of Mathematics
Karthik Nataraj, Pennsylvania State University
Department of Mathematics
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