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http://dx.doi.org/10.7858/eamj.2019.002

ON AN INVOLUTION ON PARTITIONS WITH CRANK 0  

Kim, Byungchan (School of Liberal Arts, Seoul National University of Science and Technology)
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Abstract
Kaavya introduce an involution on the set of partitions with crank 0 and studied the number of partitions of n which are invariant under Kaavya's involution. If a partition ${\lambda}$ with crank 0 is invariant under her involution, we say ${\lambda}$ is a self-conjugate partition with crank 0. We prove that the number of such partitions of n is equal to the number of partitions with rank 0 which are invariant under the usual partition conjugation. We also study arithmetic properties of such partitions and their q-theoretic implication.
Keywords
integer partitions; crank; involution;
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