Talks and Poster Presentations (with Proceedings-Entry):
M. Wallner, M. Bousquet-Melou:
"More Models of Walks Avoiding a Quadrant";
Talk: AofA 2020,
Klagenfurt;
2020-06-15
- 2020-06-20; in: "31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020)",
M. Drmota, C. Heuberger (ed.);
Leibniz International Proceedings in Informatics (LIPIcs),
159
(2020),
ISBN: 978-3-95977-147-4;
1
- 14.
English abstract:
We continue the enumeration of plane lattice paths avoiding the negative quadrant initiated by the first author in [Bousquet-Mélou, 2016]. We solve in detail a new case, the king walks, where all 8 nearest neighbour steps are allowed. As in the two cases solved in [Bousquet-Mélou, 2016], the associated generating function is proved to differ from a simple, explicit D-finite series (related to the enumeration of walks confined to the first quadrant) by an algebraic one. The principle of the approach is the same as in [Bousquet-Mélou, 2016], but challenging theoretical and computational difficulties arise as we now handle algebraic series of larger degree. We also explain why we expect the observed algebraicity phenomenon to persist for 4 more models, for which the quadrant problem is solvable using the reflection principle.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.4230/LIPIcs.AofA.2020.8
Created from the Publication Database of the Vienna University of Technology.