Cylindrical lattice paths and the Loehr-Warrington 10^n conjecture
  The following special case of a conjecture by Loehr and Warrington was proved recently by Ekhad, Vatter, and Zeilberger:   There are 10^n 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. 
Jonas Sjostrand