Y. Au

activity

20082026

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Showing 2019Show all

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math.CO2019

Some Properties and Combinatorial Implications of Weighted Small Schröder Numbers

Yu Hin Au

The $n^{th}$ small Schröder number is $s (n) = \sum_{k \geq 0} s (n, k)$ , where $s (n, k)$ denotes the number of plane rooted trees with $n$ leaves and $k$ internal nodes that ea…

math.CO2019

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…