Discrete Mathematics & Theoretical Computer Science 
We consider a large family of equivalence relations on permutations in $S_n$ that generalise 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 patternreplacing moves of prescribed form; however, we limit our focus to patterns where two elements are transposed, conditional upon the presence of a third element of suitable value and location. For some relations of this type, we compute the number of equivalence classes, determine how many $n$permutations are equivalent to the identity permutation, or characterise this equivalence class. Although our results include familiar integer sequences (e.g., Catalan, Fibonacci, and Tribonacci numbers) and special classes of permutations (layered, connected, and $123$avoiding), some of the sequences that arise appear to be new.
Source : ScholeXplorer
IsRelatedTo ARXIV 1304.5669 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1304.5669
