#### 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
##### Abstract

Let ${p}_{1},\dots ,{p}_{n}$ be a sequence of $n$ pairwise coprime positive integers, $P={p}_{1}\cdots {p}_{n}$, and $0,\dots ,m-1$ be a sequence of $m$ different colors. Let $A$ be an $n×mP$ matrix of colors in which row $i$ consists of blocks of ${p}_{i}$ 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.

##### Keywords
monochromatic column problem, Chinese remainder theorem, multiple sequence alignment problem
##### Mathematical Subject Classification 2010
Primary: 05A15, 11A07