Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity

We give a purely combinatorial proof of the Glaisher-Crofton identity which is derived from the analysis of discrete structures generated by the iterated action of the second derivative. The argument illustrates the utility of symbolic and generating function methodology of modern enumerative combin...

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Bibliographic Details
Published in:Advances in mathematical physics 2018-01, Vol.2018 (2018), p.1-9
Main Authors: Blasiak, Pawel, Penson, Karol A., Duchamp, Gérard H. E.
Format: Article
Language:English
Subjects:
Algebra
Applied mathematics
Calculus
Combinatorial analysis
Combinatorics
Mathematics
Physics
Polynomials
Quantum field theory
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Summary:We give a purely combinatorial proof of the Glaisher-Crofton identity which is derived from the analysis of discrete structures generated by the iterated action of the second derivative. The argument illustrates the utility of symbolic and generating function methodology of modern enumerative combinatorics. The paper is meant for nonspecialists as a gentle introduction to the field of graphical calculus and its applications in computational problems.
ISSN:1687-9120
1687-9139
DOI:10.1155/2018/9575626