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math.CO2008★ 7 cited
On a conjecture of Ira Gessel
Marko Petkovsek, Herbert S. Wilf
Let F(m; n1, n2) denote the number of lattice walks from (0,0) to (n1,n2), always staying in the first quadrant {(n_1,n_2); n1 >= 0, n2 >= 0} and having exactly m steps, each of wh…
math.CO2008
Counting One-Vertex Maps
Alen Orbanic, Marko Petkovsek, Tomaz Pisanski +1
The number of distinct maps (pre-maps) with a single vertex and valence is computed for any value of . The types of maps (pre-maps) that we consider depend on whether the un…