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- W2895981094 abstract "Let $s$ and $t$ be two coprime integers. Bessenrodt and Olsson obtained the number of $(overline{s},overline{t})$-cores for odd $s$ and odd $t$ by establishing a bijection between the lattice paths in $(s,t)$ Yin-Yang diagram and $(overline{s},overline{t})$-cores. In this paper, motivated by their results, we extend the definition of Yin-Yang diagram and the bijection to all possible coprime pairs $(s,t)$, then obtain that the number of $(overline{s},overline{t})$-cores is $binom{lfloor s/2 rfloor + lfloor t/2 rfloor}{lfloor s/2 rfloor}$. Furthermore, based on the identities of Chen-Huang-Wang, we determine the average size of an $(overline{s},overline{t})$-core depending on the parity of $s$, which is $(s-1) (t-1) (s+t-2)/48$ if $s$ and $t$ are both odd, or $(t-1) (s^2+st-3s+2t+2)/48$ if $s$ is even and $t$ is odd." @default.
- W2895981094 created "2018-10-26" @default.
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- W2895981094 date "2019-10-01" @default.
- W2895981094 modified "2023-09-23" @default.
- W2895981094 title "On the Average Size of an $(overline{s},overline{t})$-Core Partition" @default.
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- W2895981094 doi "https://doi.org/10.11650/tjm/181006" @default.
- W2895981094 hasPublicationYear "2019" @default.
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