# Walks avoiding a quadrant and the reflection principle

@inproceedings{BousquetMelou2021WalksAA, title={Walks avoiding a quadrant and the reflection principle}, author={Mireille Bousquet-M'elou and Michael Wallner}, year={2021} }

We continue the enumeration of plane lattice walks with small steps avoiding the negative quadrant, initiated by the first author in 2016. We solve in detail a new case, namely the king model where all eight nearest neighbour steps are allowed. The associated generating function is proved to be the sum of a simple, explicit D-finite series (related to the number of walks confined to the first quadrant), and an algebraic one. This was already the case for the two models solved by the first…

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Enumeration of three-quadrant walks via invariants: some diagonally symmetric models

- Mathematics
- 2021

In the past 20 years, the enumeration of plane lattice walks confined to a convex cone — normalized into the first quadrant — has received a lot of attention, stimulated the development of several…

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