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Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

한국고등과학원 세미나
Title A bijective proof of Amdeberhan's conjecture on the number of $(s,s+2)$-core partitions with distinct parts
Date 2018-09-13
Speaker 남하얀(University of California at Irvine)
Sponsors 2018-09-13
Host KIAS
Place 1424
Abstract Amdeberhan conjectured that the number of $(s, s + 2)$-core partitions with distinct parts for an odd integer $s$ is $2^{s-1}$. 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 $(s, s + 2)$-core partitions with distinct parts and a set of lattice paths.