Cylindrical lattice paths 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 10n zero-sum words of length 5n 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 paths.
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