62 citations · 99 across the 7 of their papers we have counts for
8 papers
The Factorial-Basis Method for Finding Definite-Sum Solutions of Linear Recurrences With Polynomial Coefficients
Antonio Jiménez-Pastor, Marko Petkovšek
The problem of finding a nonzero solution of a linear recurrence with polynomial coefficients where has the form of a definite hypergeometric sum, related to the Inver…
Convolutions of Liouvillian Sequences
Sergei A. Abramov, Marko Petkovšek, Helena Zakrajšek
While Liouvillian sequences are closed under many operations, simple examples show that they are not closed under convolution, and the same goes for d'Alembertian sequences. Nevert…
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…
New Universal Aspects of Diffusion in Strongly Chaotic Systems
Marko Robnik, Jure Dobnikar, Andrea Rapisarda +2
We study some new universal aspects of diffusion in chaotic systems, especially such having very large Lyapunov coefficients on the chaotic (indecomposable, topologically transitiv…