Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube

Yu Hin Au, Fatemeh Bagherzadeh, Murray R. Bremner

We study a two-parameter generalization of the Catalan numbers: $C_{d,p}(n)$ is the number of ways to subdivide the $d$-dimensional hypercube into $n$ rectangular blocks using orth…