Wilf-equivalence for singleton classes

J\"orgen Backelin, Julian West, Guoce Xin

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


In 1985, Rodica Simion and Frank Schmidt gave a bijection between the permutations avoiding the subsequence 123 and those avoiding 213. In other words they showed that S_n(123) <-> S_n(213). This was extended by West to S_n(12p_3...p_m) <-> S_n(21p_3...p_m) and then by West and Babson to S_n(123p_4...p_m) <-> S_n(321p_r...p_m). In this paper we give the final extension, to S_n(12...tp_{t+1}...p_m) <-> S_n(t...21p_{t+1}...p_m). Moreover we show that the same bijection applies to transversals of any Young diagram, not just a square shape.

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