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In the recent decades, core partitions and bar core partitions have attracted much attention from combinatorial researchers. In this paper, we build a bijection between $$\bar{t}$$ t ¯ -cores and self-conjugate t-cores for odd integers $$t\ge 3$$ t ≥ 3 . To this end, we first establish a bijection between $$\bar{t}$$ t ¯ -cores and self-conjugate $$(t-1)$$ ( t - 1...
The two partition functions $$p_\omega (n)$$ p ω ( n ) and $$p_\nu (n)$$ p ν ( n ) were introduced by Andrews, Dixit and Yee, which are related to the third-order mock theta functions $$\omega (q)$$ ω ( q ) and $$\nu (q)$$ ν ( q ) , respectively. Recently, Andrews and Yee analytically studied two identities that connect the refinements of $$p_\omega (n)$$ ...
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