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Wilf-equivalence for singleton classes
Stockholm University, Faculty of Science, Department of Mathematics.
2007 (English)In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 38, no 2, 133-148 p.Article in journal (Refereed) Published
Abstract [en]

Write p(1)p(2)(...)pm for the permutation matrix (delta p(i) j)(m x m). Let S-n(M) be the set of n x n permutation matrices which do not contain the m x m permutation matrix M as a submatrix. In [R. Simion, F.W. Schmidt, Restricted permutations, European J. Combin. 6 (1985) 383-406] Simion and Schmidt show bijectively that vertical bar S-n (123)vertical bar = vertical bar S-n (213)vertical bar. In the present work, we give a bi jection from S-n (12...tp(t+1)... p(m)) to S-n (t...21 p(t+1)...p(m)). This result was established for t = 2 in [J. West, Permutations with forbidden subsequences and stack-sortable permutations, PhD thesis, MIT, Cambridge, MA, 1990] and for t = 3 in [E. Babson, J. West, The permutations 123p(4)... p(t) and 321 p(4)...p(t) are Wilf-equivalent, Graphs Combin. 16 (2001) 373-3801. Moreover, if we think of n x n permutation matrices as transversals of the n by n square diagram, then we generalise this result to transversals of Young diagrams.

Place, publisher, year, edition, pages
2007. Vol. 38, no 2, 133-148 p.
Keyword [en]
permutations, permutation matrices, forbidden subsequences, bijection, Wilf-equivalence
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-57103DOI: 10.1016/j.aam.2004.11.006ISI: 000244217900001OAI: oai:DiVA.org:su-57103DiVA: diva2:415740
Note
authorCount :3Available from: 2011-05-09 Created: 2011-05-03 Last updated: 2017-12-11Bibliographically approved

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