2009/09/29 by Edray Herber Goins, Talitha Washington, Goins, Edray Herber +2
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #math.CO #msc:05A15 #msc:05A17
paper · pdf · doi:10.48550/arxiv.0909.5459
arxiv created 2009/09/29 · arxiv updated 2009/12/01
Let \mathcal S be a subset of the positive integers, and M be a positive integer. Mohammad K. Azarian, inspired by work of Tony Colledge, considered the number of ways to climb a staircase containing n stairs using "step-sizes" s ∈ \mathcal S and multiplicities at most M. In this exposition, we find a solution via generating functions, i.e., an expression which counts the number of partitions n = ∑s ∈ \mathcal S ms s satisfying 0 ≤ ms ≤ M. We then use this result to answer a series of questions posed by Azarian, thereby showing a link with ten sequences listed in the On-Line Encyclopedia of Integer Sequences. We conclude by posing open questions which seek to count the number of compositions of n.