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Minimal factorizations of permutations into star transpositions |
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| Authors: | J. Irving A. Rattan |
| Affiliation: | a Department of Mathematics and Computing Science, St Mary’s University, Halifax, NS, B3H 3C3, Canada b Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA |
| Abstract: | We give a compact expression for the number of factorizations of any permutation into a minimal number of transpositions of the form  . This generalizes earlier work of Pak in which substantial restrictions were placed on the permutation being factored. Our result exhibits an unexpected and simple symmetry of star factorizations that has yet to be explained in a satisfactory manner. |
| Keywords: | Factorizations Permutations Star transpositions Symmetrical group |
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