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Generating-Tree Isomorphisms for Pattern-Avoiding Involutions

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Abstract

We show that for k ≥ 5 and the permutations τ k = (k − 1)k(k − 2). . .312 and J k = k(k − 1). . .21, the generating tree for involutions avoiding the pattern τ k is isomorphic to the generating tree for involutions avoiding the pattern J k . This implies a family of Wilf equivalences for pattern avoidance by involutions.

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Authors and Affiliations

  1. Department of Computer Science, Colgate University, 13 Oak Drive, Hamilton, NY, 13346, USA

    Aaron D. Jaggard

  2. Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI, 48109-1043, USA

    Joseph J. Marincel

Authors
  1. Aaron D. Jaggard
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  2. Joseph J. Marincel
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Correspondence to Aaron D. Jaggard.

Additional information

Partially supported by NSF award DMS–0239996 and by NSA award H98230-09-1-0014. This work was carried out in part while Jaggard was at the Department of Mathematics at Tulane University and in part while Marincel was a participant in an REU at Tulane University. Jaggard is also affiliated with the DIMACS Center, Rutgers University.

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Jaggard, A.D., Marincel, J.J. Generating-Tree Isomorphisms for Pattern-Avoiding Involutions. Ann. Comb. 15, 437–448 (2011). https://doi.org/10.1007/s00026-011-0101-x

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  • DOI: https://doi.org/10.1007/s00026-011-0101-x

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