Journal of Combinatorics

Volume 6 (2015)

Number 1–2

A simple proof of a theorem of Schmerl and Trotter for permutations

Pages: 47 – 54



Robert Brignall (Department of Mathematics and Statistics, The Open University, Milton Keynes, United Kingdom)

Vincent Vatter (Department of Mathematics, University of Florida, Gainesville, Fl., U.S.A.)


When specialized to the context of permutations, Schmerl and Trotter’s Theorem states that every simple permutation which is not a parallel alternation contains a simple permutation with one fewer entry. We give an elementary proof of this result.

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Published 20 March 2015