(README in progress. Completion coming soon.)
Research project from the Kinnaird Institute Research Program at Millsaps College, supervised by Dr. Alex Rice and Dr. Priyadarshi Dey, testing a conjecture from Fredrickson-Sweet's 2000 paper that speculates certain 5-colored values of N <= 160 fail to produce "weakly palindromic" coloring.
A Schur triple is a group of three positive integers (x,y,z) such that x + y = z. They are prevalent in Ramsey theory, which studies the patterns of numbers when grouped/colored in finite sets. A monochromatic Schur triple (MST) is where all three integers (x + y = z) share the same color in a partitioned set. Schur's Theorem proves an MST is guaranteed to appear at least once if you color N = {1,2,...,N} up to a large enough number, S(r), using r amount of colors. For example, it was found in 2017 that for five colors, S(5) = 161, meaning all possible coloring of N = 161 is guaranteed to have at least one MST. This also proves that there exists at least one coloring for each 5-coloring of N < 161 where there are no MSTs.
Similarly, a modular monochromatic Schur triple (MMST) changes the condition of addition equation to a modular setting, satisfying x + y is congruent to z % N.