Séminaire Lotharingien de Combinatoire, 82B.26 (2019), 12 pp.

Nicholas R. Beaton, Aleksander L. Owczarek, and Ruijie Xu

Quarter-plane lattice paths with interacting boundaries: Kreweras and friends

Abstract. We study lattice paths in the quarter-plane which accrue weights with each visit to the x-axis, the y-axis and the origin. In particular, we address two cases which were only partially solved in a recent work by Beaton, Owczarek and Rechnitzer (2018): Kreweras and reverse Kreweras paths. Without weights these are two of the famous algebraic quarter-plane models. We show that the reverse Kreweras model remains algebraic for all possible weights, while the nature of the Kreweras model appears to depend on the value of the weights and the endpoint of the paths.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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