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Wilf-equivalence fo...
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- permutations
- permutation matrices
- forbidden subsequences
- bijection
- Wilf-equivalence
- MATHEMATICS
- MATEMATIK
Publication and Content Type
- ref (subject category)
- art (subject category)
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