论文标题
关于Andrews-Macmahon定理的注释
A note on Andrews-MacMahon theorem
论文作者
论文摘要
对于正整数$ r $，乔治·安德鲁斯（George Andrews）证明了$ n $的分区集至少为$ 2R + 1 $，均与$ n $的分区集合，其中奇数零件一致，其中奇数 + $ 2R + 1 $ modulo $ 4r $ 4r + 2 $ 2 $。这是Macmahon定理的扩展（$ r = 1 $）。安德鲁斯（Andrews），埃里克森（Ericksson），彼得罗夫（Petrov）和罗米克（Romik）提供了麦克马洪定理的族裔证明。尽管有几种双线，直到最近，它们都没有安德鲁斯 - 埃里克森 - 佩特罗夫 - 罗米克射击的精神。安德鲁斯定理最近也已扩展。我们的目标是在Andrews-Ericksson-Petrov-Romik射击的精神上对这一进一步扩展进行广泛的徒图映射。
For a positive integer $r$, George Andrews proved that the set of partitions of $n$ in which odd multiplicities are at least $2r + 1$ is equinumerous with the set of partitions of $n$ in which odd parts are congruent to $2r + 1$ modulo $4r + 2$. This was given as an extension of MacMahon's theorem ($r = 1$). Andrews, Ericksson, Petrov and Romik gave a bijective proof of MacMahon's theorem. Despite several bijections being given, until recently, none of them was in the spirit of Andrews-Ericksson-Petrov-Romik bijection. Andrews' theorem has also been extended recently. Our goal is to give a generalized bijective mapping of this further extension in the spirit of Andrews-Ericksson-Petrov-Romik bijection.
