3 citations · 3 across the 5 of their papers we have counts for
4 papers · 1 filter
On the finiteness of the group associated with weighted walks in multidimensional orthants
Andrew Elvey Price, Emmanuel Humbert, Kilian Raschel
In the study of walks with small steps confined to multidimensional orthants, a certain group of transformations plays a central role. In particular, several techniques to potentia…
Bivariate asymptotics via random walks: application to large genus maps
Andrew Elvey Price, Wenjie Fang, Baptiste Louf +1
We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two r…
Refined enumeration of planar Eulerian orientations
Mireille Bousquet-Mélou, Andrew Elvey Price
We address the enumeration of Eulerian orientations of 4-valent planar maps according to three parameters: the number of vertices, the number of alternating vertices (having in/out…
Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness
Thomas Dreyfus, Andrew Elvey Price, Kilian Raschel
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in…