We consider a large family of equivalence relations on the symmetric group of permutations of n that generalize those discovered by Knuth in his study of the RobinsonSchensted correspondence. In our most general setting, two permutations are equivalent if one can be obtained from the other by a sequence of pattern-replacing moves of prescribed form; however, we limit our focus to patterns where...

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In this paper, we will show how certain Hecke correspondences on modular curves may be characterized by their geometrical properties. We introduce the notion of a cuspidal correspondence and of an almost unramified correspondence (Definition 5) and prove (Theorem 1) that an irreducible almost unramified cuspidal correspondence on a modular curve is a modular correspondence. By considering the b...