New Equivalences for Pattern Avoidance for Involutions
نویسندگان
چکیده
We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard’s conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of S5, S6, and S7 for both permutations and involutions.
منابع مشابه
Generating-tree isomorphisms for pattern-avoiding involutions∗
We show that for k ≥ 5 and the permutations τk = (k − 1)k(k − 2) . . . 312 and Jk = k(k − 1) . . . 21, the generating tree for involutions avoiding the pattern τk is isomorphic to the generating tree for involutions avoiding the pattern Jk. This implies a family of Wilf equivalences for pattern avoidance by involutions; at least the first member of this family cannot follow from any type of pre...
متن کاملNew Equivalences for Pattern Avoiding Involutions
We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard’s conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of S5, S6, and S7 for involutions.
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Let In(π) denote the number of involutions in the symmetric group Sn which avoid the permutation π. We say that two permutations α, β ∈ Sj may be exchanged if for every n, k, and ordering τ of j + 1, . . . , k, we have In(ατ) = In(βτ). Here we prove that 12 and 21 may be exchanged and that 123 and 321 may be exchanged. The ability to exchange 123 and 321 implies a conjecture of Guibert, thus co...
متن کاملPrefix Exchanging and Pattern Avoidance by Involutions
Let In(π) denote the number of involutions in the symmetric group Sn which avoid the permutation π. We say that two permutations α, β ∈ Sj may be exchanged if for every k and ordering τ of j + 1, . . . , k, we have In(ατ) = In(βτ) for every n. Here we prove that 12 and 21 may be exchanged and that 123 and 321 may be exchanged. The first of these theorems gives a number of known results for patt...
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