1Brown University 2Instituto de Matematica e Estatistica, Universidade de S\~ao Paulo 3LSS/CentraleSupelec, Universe Paris Sud, FranceandDpt of Mathematics, Tulane University, New Orleans, USA 4University of Maryland
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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.
1
Brown University
2
Instituto de Matematica e Estatistica, Universidade de S\~ao Paulo
3
LSS/CentraleSupelec, Universe Paris Sud, FranceandDpt of Mathematics, Tulane University, New Orleans, USA
4
University of Maryland
@article{10_37236_8788,
author = {Quang-Nhat Le and Sinai Robins and Christophe Vignat and Tanay Wakhare},
title = {A continuous analogue of lattice path enumeration},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8788},
zbl = {1420.05080},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8788/}
}
TY - JOUR
AU - Quang-Nhat Le
AU - Sinai Robins
AU - Christophe Vignat
AU - Tanay Wakhare
TI - A continuous analogue of lattice path enumeration
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8788/
DO - 10.37236/8788
ID - 10_37236_8788
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%0 Journal Article
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%A Sinai Robins
%A Christophe Vignat
%A Tanay Wakhare
%T A continuous analogue of lattice path enumeration
%J The electronic journal of combinatorics
%D 2019
%V 26
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Quang-Nhat Le; Sinai Robins; Christophe Vignat; Tanay Wakhare. A continuous analogue of lattice path enumeration. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8788
