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Combinatorics of nondeterministic walks of the Dyck and Motzkin type [article]

Elie De Panafieu, Mohamed Lamine Lamali, Michael Wallner (TU Wien)
2018 arXiv   pre-print
We introduce our new model on Dyck steps with the nondeterministic step set --1, 1, --1, 1 and Motzkin steps with the nondeterministic step set --1, 0, 1, --1, 0, --1, 1, 0, 1, --1, 0, 1.  ...  In the particular cases of Dyck and Motzkin steps, we also compute the asymptotic probability that at least one of those parallel walks is a meander (stays nonnegative) or an excursion (stays nonnegative  ...  Conclusion In this paper we introduced nondeterministic lattice paths and solved the asymptotic counting problem for such walks of the Dyck and Motzkin type.  ... 
arXiv:1812.06650v1 fatcat:2u7wnqv3jzgxdeaslbwhmnjsgm

Combinatorics of nondeterministic walks of the Dyck and Motzkin type [chapter]

Élie de Panafieu, Mohamed Lamine Lamali, Michael Wallner
2019 2019 Proceedings of the Sixteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)  
We introduce our new model on Dyck steps with the nondeterministic step set {{−1}, {1}, {−1, 1}} and Motzkin steps with the nondeterministic step set For general lists of step sets and a given length,  ...  In the particular cases of Dyck and Motzkin steps, we also compute the asymptotic probability that at least one of those parallel walks is a meander (stays nonnegative) or an excursion (stays nonnegative  ...  Conclusion In this paper we introduced nondeterministic lattice paths and solved the asymptotic counting problem for such walks of the Dyck and Motzkin type.  ... 
doi:10.1137/1.9781611975505.1 dblp:conf/analco/PanafieuLW19 fatcat:xyvol364ijd2rlev6ebu2ngezm