Combinatorial interpretation and proof of Glaisher-Crofton identity
Pawel Blasiak, Gerard H. E. Duchamp, Andrzej Horzela, Karol A. Penson
TL;DR
This paper provides a combinatorial proof of the Glaisher-Crofton identity, demonstrating the application of modern enumerative combinatorics and generating functions to analyze structures generated by iterated derivatives.
Contribution
It offers a new combinatorial proof of the Glaisher-Crofton identity using symbolic and generating function methods.
Findings
Combinatorial proof of Glaisher-Crofton identity
Application of generating functions to derivative-based structures
Illustration of modern enumerative combinatorics in analysis
Abstract
We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function methodology of modern enumerative combinatorics and their applications to computational problems.
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