A combinatorial construction for two formulas in Slater's list

Kurşungöz, Kağan (2021) A combinatorial construction for two formulas in Slater's list. International Journal of Number Theory, 17 (3). pp. 655-663. ISSN 1793-0421 (Print) 1793-7310 (Online)

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We set up a combinatorial framework for inclusion-exclusion on the partitions into distinct parts to obtain an alternative generating function of partitions into distinct and non-consecutive parts. In connection with Rogers-Ramanujan identities, the generating function yields two formulas in Slater's list. The same formulas were constructed by Hirschhorn. Similar formulas were obtained by Bringmann, Mahlburg and Nataraj. We also use staircases to give alternative triple series for partitions into d-distinct parts for any d ≥ 2.
Item Type: Article
Uncontrolled Keywords: Integer partition; partition generating function; Rogers-Ramanujan identities; Slater's list
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Kağan Kurşungöz
Date Deposited: 02 Sep 2022 23:15
Last Modified: 02 Sep 2022 23:15
URI: https://research.sabanciuniv.edu/id/eprint/43377

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