Cylindrical lattice walks and the Loehr–Warrington 10n10n conjecture

The following special case of a conjecture by Loehr and Warrington was proved recently by Ekhad, Vatter, and Zeilberger:There are 10n10n zero-sum words of length 5n5n 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.