Enumerations of plane trees with multiple edges and Raney lattice paths

to representation the complex technical systems, we propose the use of fuzzy GH-models based on graphs, which differ from known that allow to take into account, in addition to the same type of edges, different types of edges and multiple edges in the form of a vector. The paper notes the advantages of GH-graphs due to the use of edges in the form of a vector, which reduces the time spent on calculations on graphs and at the same time takes into account the necessary relations in the system. The classification of edges in GH-graphs is performed, due to the need to use all possible relations between the objects of the system.

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Analytic Combinatorics of Lattice Paths with Forbidden Patterns: Enumerative Aspects

Language and Automata Theory and Applications - Lecture Notes in Computer Science ◽

10.1007/978-3-319-77313-1_15 ◽

2018 ◽

pp. 195-206 ◽

Cited By ~ 3

Author(s):

Andrei Asinowski ◽

Axel Bacher ◽

Cyril Banderier ◽

Bernhard Gittenberger

Keyword(s):

Lattice Paths ◽

Analytic Combinatorics ◽

Forbidden Patterns

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LONDON'S PLANE TREES

The Lancet ◽

10.1016/s0140-6736(54)90480-8 ◽

1954 ◽

Vol 264 (6840) ◽

pp. 709

Author(s):

Desmond O'Neill

Keyword(s):

Plane Trees

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Random sampling of lattice paths with constraints, via transportation

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.2783 ◽

2010 ◽

Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽

Author(s):

Lucas Gerin

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Random Sampling ◽

Optimal Transport ◽

Lattice Paths ◽

Dimensional Lattice ◽

One Dimensional ◽

Contraction Property ◽

International Audience

International audience We build and analyze in this paper Markov chains for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. These chains are easy to implement, and sample an "almost" uniform path of length $n$ in $n^{3+\epsilon}$ steps. This bound makes use of a certain $\textit{contraction property}$ of the Markov chain, and is proved with an approach inspired by optimal transport.

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