A Continuous Analogue of Lattice Path Enumeration

Abstract : Following the work of Cano and Díaz, we consider a continuous analog of lattice path enumeration. This process allows us to define a continuous version of many discrete objects that count certain types of lattice paths. As an example of this process, we define continuous versions of binomial and multinomial coefficients, and describe some identities and partial differential equations that they satisfy. Finally, as an important byproduct of these continuous analogs, we illustrate a general method to recover discrete combinatorial quantities from their continuous analogs, via an application of the Khovanski-Puklikov discretizing Todd operators.
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Contributor : Christophe Vignat <>
Submitted on : Wednesday, October 2, 2019 - 12:07:00 PM
Last modification on : Friday, October 4, 2019 - 1:47:44 AM


  • HAL Id : hal-02303434, version 1


Quang-Nhat Le, Sinai Robins, Christophe Vignat, Tanay Wakhare. A Continuous Analogue of Lattice Path Enumeration. The Electronic Journal of Combinatorics, Open Journal Systems, 2019. ⟨hal-02303434⟩



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