A continuous analogue of lattice path enumeration

2017/07/06 by Tanay Wakhare, Christophe Vignat, Wakhare, T. +5 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1707.01616

openalex publication_date 2017/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following the work of Cano and Diaz, we consider a continuous analog of lattice path enumeration. This allows us to define a continuous version of any discrete object that counts certain types of lattice paths. We define continuous versions of binomials and multinomials, and describe some identities and partial differential equations they satisfy. Finally, we illustrate a general process to recover discrete combinatorial quantities from their continuous analogs.

Citations

• Indirect Influences on Directed Manifolds
• Continuous Analogues for the Binomial Coefficients and the Catalan Numbers

Cited by

• A Continuous Analogue for Young Diagrams
• A Continuous Analogue of Lattice Path Enumeration: Part II

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• A Continuous Analogue of Lattice Path Enumeration: Part II
• Continuous Analogues for the Binomial Coefficients and the Catalan Numbers
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