5 research outputs found

    Enumerating two permutation classes by number of cycles

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    We enumerate permutations in the two permutation classes Avn(312,4321)\text{Av}_n(312, 4321) and Avn(321,4123)\text{Av}_n(321, 4123) by the number of cycles each permutation admits. We also refine this enumeration with respect to several statistics

    Pattern-restricted permutations of small order

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    We enumerate 132-avoiding permutations of order 3 in terms of the Catalan and Motzkin generating functions, answering a question of B\'{o}na and Smith from 2019. We also enumerate 231-avoiding permutations that are composed only of 3-cycles, 2-cycles, and fixed points.Comment: 16 page
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