62 citations · 99 across the 7 of their papers we have counts for
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Vertex and edge orbits of Fibonacci and Lucas cubes
Ali Reza Ashrafi, Jernej Azarija, Khadijeh Fathalikhani +2
The Fibonacci cube is obtained from the -cube by removing all the vertices that contain two consecutive 1s. If, in addition, the vertices that start and end with 1 a…
Quantum random walk on the integer lattice: examples and phenomena
Andrew Bressler, Torin Greenwood, Robin Pemantle +1
We apply results from Baryshnikov, Brady, Bressler and Pemantle (2008) to compute limiting probability profiles for various quantum random walks in one and two dimensions. Using an…
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…
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…
Walks confined in a quadrant are not always D-finite
Mireille Bousquet-Melou, Marko Petkovsek
We consider planar lattice walks that start from a prescribed position, take their steps in a given finite subset of Z^2, and always stay in the quadrant x >= 0, y >= 0. We first g…