Counting Lattice Paths via a New Cycle Lemma
نویسندگان
چکیده
منابع مشابه
Counting Lattice Paths via a New Cycle Lemma
Let α, β,m, n be positive integers. Fix a line L : y = αx + β, and a lattice point Q = (m,n) on L. It is well known that the number of lattice paths from the origin to Q which touches L only at Q is given by β m+ n “m+ n m ” . We extend the above formula in various ways, in particular, we consider the case when α and β are arbitrary positive reals. The key ingredient of our proof is a new varia...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2012
ISSN: 0895-4801,1095-7146
DOI: 10.1137/100796431