2015/09/21 by Caleb Ji, Tanya Khovanova, Ji, Caleb +5
Mathematics · #11B99 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:11B99
paper · pdf · doi:10.48550/arxiv.1509.06093
16 pages, 1 figure
arxiv created 2015/09/21 · arxiv updated 2015/09/22
In this paper, we consider a game played on a rectangular m × n gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along existing grid lines, until just mn individual squares remain. This paper enumerates the number of ways to break an m × n bar, which we call chocolate numbers, and introduces four new sequences related to these numbers. Using various techniques, we prove interesting divisibility results regarding these sequences.