A human proof for a generalization of Shalosh B. Ekhad’s 10 Lattice Paths Theorem

نویسندگان

  • Nicholas A. Loehr
  • Bruce E. Sagan
  • Gregory S. Warrington
چکیده

Consider lattice paths in Z taking unit steps north (N) and east (E). Fix positive integers r, s and put an equivalence relation on points of Z by letting v,w be equivalent if v − w = l(r, s) for some l ∈ 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 r )n . We prove this conjecture when s = 2.

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تاریخ انتشار 2008