2005/10/04 by Nicholas A. Loehr, Loehr, Nicholas A., Bruce E. Sagan +3
Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15
paper · pdf · doi:10.48550/arxiv.math/0510079
9 pages, 6 figures
arxiv created 2005/10/04 · arxiv updated 2009/12/01
Consider lattice paths in Z2 taking unit steps north (N) and east (E). Fix positive integers r,s and put an equivalence relation on points of Z2 by letting v,w be equivalent if v - w = m (r,s) for some m in Z. Call a lattice path valid if whenever it enters a point v with an E-step, then any further points of the path in the class of v are also entered with an E-step. Loehr and Warrington conjectured that the number of valid paths from (0,0) to (nr,ns) is (r+s choose r)n. We prove this conjecture when s = 2.