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

Pawel Blasiak, Gérard H. E. Duchamp, Karol A. Penson
2018 Advances in Mathematical Physics  
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.
doi:10.1155/2018/9575626 fatcat:2dcznlb6fzfs3iaqn7ckktyajq