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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Factorization of banded permutations


Author: Greta Panova
Journal: Proc. Amer. Math. Soc. 140 (2012), 3805-3812
MSC (2010): Primary 05A05, 20B99; Secondary 15A23, 15B99, 65T50
Published electronically: March 19, 2012
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Abstract: We consider the factorization of permutations into bandwidth 1 permutations, which are products of mutually nonadjacent simple transpositions. We exhibit an upper bound on the minimal number of such factors and thus prove a conjecture of Gilbert Strang: a banded permutation of bandwidth $ w$ can be represented as the product of at most $ 2w-1$ permutations of bandwidth 1. An analogous result holds also for infinite and cyclically banded permutations.


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Additional Information

Greta Panova
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Address at time of publication: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095
Email: greta.panova@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11411-X
PII: S 0002-9939(2012)11411-X
Received by editor(s): December 24, 2010
Received by editor(s) in revised form: May 6, 2011
Published electronically: March 19, 2012
Communicated by: Jim Haglund
Article copyright: © Copyright 2012 American Mathematical Society