Year: 2025
Type: article
Abstract: Pascal’s triangle is a classical mathematical construct, historically studied for centuries, that organises binomial coefficients in a triangular array and serves as a cornerstone in combinatorics, algebra, and number theory. Herein, we propose to model it with Petri nets, a formal specification technique derived from discrete event systems. A minimal Petri net is created that generates Pascal’s triangle under a simple arithmetic rule. Token counts in each place coincide with binomial coefficients, providing a direct combinatorial interpretation. Two other classical structures emerge from this model: by colouring tokens depending on their parity, the Sierpiński triangle appears; by routing tokens randomly at each branching, the binomial distribution arises, converging to a Gaussian limit as depth increases. As a result, a single Petri construction unifies three mathematical objects: Pascal’s Triangle, Sierpiński’s Triangle, and the Gaussian distribution. This connection illustrates the invaluable potential of Petri nets as unifying tools for modelling discrete mathematical structures and beyond.
Source: Symmetry
DOI: 10.3390/sym17122181
Authors: David Mailland, Iwona Grobelna
Institution: University of Zielona Góra
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4417454742