对Shalosh B. Ekhad的10^n格路定理
A human proof for a generalization of Shalosh B. Ekhad's 10^n Lattice Paths Theorem
摘要：
考虑Z^2中的格点路径，向北（N）和向东（E）各取一个单位步长。固定正整数r，s，并在Z ^2上的点上建立一个等价关系，设v，w是等价的，如果v - w = m（r，s），其中m在Z中。称一条格路有效，如果每当它以E步进入一个点v时，那么v类中的任何其他点也以E步进入。Loehr和Warrington证明了从（0，0）到（nr，ns）的有效路径数是（r+s choose r）^n。当s = 2时，我们证明了这个猜想。
英文摘要：
Consider lattice paths in Z^2 taking unit steps north (N) and east (E). Fix positive integers r,s and put an equivalence relation on points of Z^2 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
