On non-squashing partitions Original Research Article

A partition image with image is called non-squashing if image for image. Hirschhorn and Sellers showed that the number of non-squashing partitions of image is equal to the number of binary partitions of image. Here we exhibit an explicit bijection between the two families, and determine the number of non-squashing partitions with distinct parts, with a specified number of parts, or with a specified maximal part. We use the results to solve a certain box-stacking problem.