Xi Sisi Shen 1,3 Department of Mathematics and Statistics McGill University Montreal, Canada Aaron Williams 2 Department of Mathematics and Statistics McGill University Montreal, Canada 1 Introduction Let Π(n) be the set of permutations of [n]={1, 2,...,n} written as strings in one-line notation. For example, Π(3)={123, 132, 213, 231, 312, 321}. A permutation Gray code is an order of Π(n) in which successive permutations 1 Email: xi.shen@mail.mcgill.ca 2 Email: haron@uvic.ca 3 Research partially funded by the Institut des Sciences Math´ ematiques. Abstract We give the n! permutations of [n]={1, 2,...,n} a cyclic order inspired by the chil- dren’s game of Hot Potato. Our order is a transposition Gray code, meaning that consecutive permutations differ by a single transposition. Furthermore, each trans- position is restricted in two ways: (1) It must transpose value n (the “hot potato”); (2) It must transpose positions that are circularly adjacent or semi-adjacent. In other words, if each permutation is written circularly, then our order repeatedly transposes the value n with a value that is one or two positions to its left or right. Keywords: Gray code, permutation, star transposition, adjacent transposition, vertex transitive graph, Hamilton cycle, Lov´ asz conjecture A ‘Hot Potato’ Gray Code for Permutations Available online at www.sciencedirect.com Electronic Notes in Discrete Mathematics 44 (2013) 89–94 1571-0653/$ – see front matter © 2013 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm http://dx.doi.org/10.1016/j.endm.2013.10.014