Geodesic
Enumerating lattice paths touching or crossing the diagonal at a given number of lattice points
Michael Z. Spivey1
1University of Puget Sound
The electronic journal of combinatorics, Tome 19 (2012) no. 3
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We give bijective proofs that, when combined with one of the combinatorial proofs of the general ballot formula, constitute a combinatorial argument yielding the number of lattice paths from $(0,0)$ to $(n,rn)$ that touch or cross the diagonal $y = rx$ at exactly $k$ lattice points. This enumeration partitions all lattice paths from $(0,0)$ to $(n,rn)$. While the resulting formula can be derived using results from Niederhausen, the bijections and combinatorial proof are new.
DOI : 10.37236/2477
Classification : 05A15, 05A19
Mots-clés : lattice path, bijection

Michael Z. Spivey  1

1 University of Puget Sound 
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Michael Z. Spivey. Enumerating lattice paths touching or crossing the diagonal at a given number of lattice points. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2477

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