{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86982"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86982","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Some Results on the Congruential and Gap -Theoretic Study of Partition Functions","abstract":"\"Recently, several authors have been treating partitions by considering the gaps between their consecutive parts. Many of the existing results involving \"\"partitions with parts in the gaps\"\" bear a striking resemblance to certain weighted partition identities that also arise from the gaps of partitions. In this thesis, we provide combinatorial proofs of several results from the literature involving partitions with parts in the gaps, and in doing so, we discover many generalizations of these original results. 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