MacMahon’s statistics on higher-dimensional partitions
MacMahon’s statistics on higher-dimensional partitions
Abstract We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between d -dimensional partitions and d -dimensional arrays of nonnegative integers. This bijection has a number of important applications. We introduce a statistic on d -dimensional partitions, called the corner-hook volume, whose …