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- W4366404037 abstract "For 80 years, Dysonâs rank has been known as the partition statistic that witnesses the first two of Ramanujanâs celebrated congruences for the ordinary partition function. In this paper, we show that Dysonâs rank actually witnesses families of partition congruences modulo every prime $ell$. This comes from an in-depth study of when a âmultiplicity-based statisticâ is a crank witnessing congruences for the function $pbig (n,mbig )$, which enumerates partitions of $n$ with parts of size at most $m$. We also show that as the modulus $ell$ increases, there is an ever-growing collection of distinct multiplicity-based cranks witnessing these same families." @default.
- W4366404037 created "2023-04-21" @default.
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- W4366404037 date "2023-04-19" @default.
- W4366404037 modified "2023-10-12" @default.
- W4366404037 title "Cranks for partitions with bounded largest part" @default.
- W4366404037 doi "https://doi.org/10.1090/proc/16399" @default.
- W4366404037 hasPublicationYear "2023" @default.
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