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Minimal Factorizations of Permutations into Star Transpositions

Abstract : We give a compact expression for the number of factorizations of any permutation into a minimal number of transpositions of the form $(1 i)$. Our result generalizes earlier work of Pak ($\textit{Reduced decompositions of permutations in terms of star transpositions, generalized catalan numbers and k-ary trees}$, Discrete Math. $\textbf{204}$:329―335, 1999) in which substantial restrictions were placed on the permutation being factored.
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J. Irving, A. Rattan. Minimal Factorizations of Permutations into Star Transpositions. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.507-512. ⟨hal-01185128⟩

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