Vol. 12, No. 8, 2019

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The monochromatic column problem with a prime number of colors

Loran Crowell and Steve Szabo

Vol. 12 (2019), No. 8, 1415–1422

Let p1,,pn be a sequence of n pairwise coprime positive integers, P = p1pn, and 0,,m 1 be a sequence of m different colors. Let A be an n × mP matrix of colors in which row i consists of blocks of pi consecutive entries of the same color with colors 0 through m 1 repeated cyclically. The monochromatic column problem is to determine the number of columns of A in which every entry is the same color. The solution for a prime number of colors is provided.

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monochromatic column problem, Chinese remainder theorem, multiple sequence alignment problem
Mathematical Subject Classification 2010
Primary: 05A15, 11A07
Received: 5 July 2019
Revised: 6 August 2019
Accepted: 12 August 2019
Published: 25 October 2019

Communicated by Kenneth S. Berenhaut
Loran Crowell
Eastern Kentucky University
Richmond, KY
United States
Steve Szabo
Eastern Kentucky University
Richmond, KY
United States