Quasirandom Graphs and the Pantograph Equation

Quasirandom Graphs and the Pantograph Equation

The pantograph differential equation and its solution, the deformed exponential function, are remarkable objects that appear in areas as diverse as combinatorics, number theory, statistical mechanics, and electrical engineering. In this article, we describe a new surprising application of these obje...

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Veröffentlicht in:The American mathematical monthly 2021-08, Vol.128 (7), p.630-639
Hauptverfasser: Shapira, Asaf, Tyomkyn, Mykhaylo
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Differential equations
Exponential functions
Graph theory
Graphs
Mathematical models
Mathematics
MSC: Primary 05C35
Number theory
Original
Pantographs
Secondary 05C80
Statistical mechanics
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Beschreibung
Zusammenfassung:The pantograph differential equation and its solution, the deformed exponential function, are remarkable objects that appear in areas as diverse as combinatorics, number theory, statistical mechanics, and electrical engineering. In this article, we describe a new surprising application of these objects in graph theory, by showing that the set of all cliques is not forcing for quasirandomness. This provides a natural example of an infinite family of graphs, which is not forcing, and answers a natural question posed by P. Horn.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2021.1926187