Differential Posets and k-ribbon Tableaux
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In this study we examine a class of partially ordered sets (posets). Differential posets were first introduced by R. Stanley in 1988 and are a group of posets which meet criteria set forth by Stanley. After examining Young's lattice, Stanley's classic example of a 1-differential poset, we investigate the posets created by 2-ribbons and 3-ribbons. In a 2001 paper M. Shimozono and D. White prove indirectly through the use of a 2-quotient that a 2-ribbon tableaux is 2-differential. Using a direct combinatorial proof we show that for the k = 2 and k = 3 case that k-ribbon tableaux are k-differential.