Panova, Greta Factorization of banded permutations. (English) Zbl 1270.05003 Proc. Am. Math. Soc. 140, No. 11, 3805-3812 (2012). Summary: 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. Cited in 3 Documents MSC: 05A05 Permutations, words, matrices 20B99 Permutation groups 15A23 Factorization of matrices 15B99 Special matrices 65T50 Numerical methods for discrete and fast Fourier transforms Keywords:mutually nonadjacent simple transpositions; bandwidth 1 permutations; banded permutations PDFBibTeX XMLCite \textit{G. Panova}, Proc. Am. Math. Soc. 140, No. 11, 3805--3812 (2012; Zbl 1270.05003) Full Text: DOI arXiv References: [1] Chase Albert, Chi-Kwong Li, Gilbert Strang, and Gexin Yu, Permutations as product of parallel transpositions, SIAM J. Discrete Math. 25 (2011), no. 3, 1412 – 1417. · Zbl 1237.05002 · doi:10.1137/100807478 [2] Anders Björner and Francesco Brenti, Combinatorics of Coxeter groups, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005. · Zbl 1110.05001 [3] Martianus Frederic Ezerman and Michael Daniel Samson, Factoring Permutation Matrices into a Product of Tridiagonal Matrices (2010), available at arXiv:1007.3467. [4] Jacob E. Goodman, Proof of a conjecture of Burr, Grünbaum, and Sloane, Discrete Math. 32 (1980), no. 1, 27 – 35. · Zbl 0444.05029 · doi:10.1016/0012-365X(80)90096-5 [5] Gilbert Strang, Fast transforms: banded matrices with banded inverses, Proc. Natl. Acad. Sci. USA 107 (2010), no. 28, 12413 – 12416. · Zbl 1205.65348 · doi:10.1073/pnas.1005493107 [6] Gilbert Strang, Groups of banded matrices with banded inverses, Proc. Amer. Math. Soc. 139 (2011), no. 12, 4255 – 4264. · Zbl 1241.15011 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.