Cylindrical lattice walks and the Loehr–Warrington 10n conjecture

Abstract

The following special case of a conjecture by Loehr and Warrington was proved recently by Ekhad, Vatter, and Zeilberger: There are 1 0 n zero-sum words of length 5 n in the alphabet {+3,−2} such that no zero-sum consecutive subword that starts with +3 may be followed immediately by −2. We give a simple bijective proof of the conjecture in its original and more general setting. To do this we reformulate the problem in terms of cylindrical lattice walks.