2011/07/14 by Patrick Devlin, Devlin, Patrick · 1 citation
Mathematics · #05D05 (Primary) 11B75 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05D05 #msc:11B75
paper · pdf · doi:10.48550/arxiv.1107.2954
19 pages, submitted to Integers in July 2011
arxiv created 2011/07/14 · arxiv updated 2011/07/18
In this paper, we consider a certain variation of the "isoperimetric problem" adopted for subsets of nonnegative integers. More specifically, we explore the sequence P(n) as described in OEIS A186053. We provide the first exact formulas for P(n) including multiple recursive relations involving auxiliary functions as well as concise and satisfying representations and quasi-explicit formulas. We also discuss some of the intricate fractal-like symmetry of the sequence as well as the development of algorithms for computing P(n). We conclude with open questions for further research.