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Amdeberhan conjectured that the number of -core partitions with distinct parts for an odd integer is . This conjecture was first proved by Yan, Qin, Jin and Zhou, then subsequently by Zaleski and Zeilberger. Since the formula for the number of such core partitions is so simple one can hope for a bijective proof. We give the first direct bijective proof of this fact by establishing a bijection between the set of -core partitions with distinct parts and a set of lattice paths. 相似文献
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The Ramanujan Journal - In two papers, Little and Sellers introduced an exciting new combinatorial method for proving partition identities which is not directly bijective. Instead, they consider... 相似文献
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