Symmetric function and application of a combination of nature
|School||Lanzhou University of Technology|
|Keywords||Symmetric function Pascal matrix Stirling matrix Vandermonde matrix Elementary symmetric polynomial matrix Completely symmetric polynomial matrix|
Symmetric function theory is the algebraic combinatorics is an important area of research, it is mainly research symmetry group and algebraic properties of symmetric polynomials and combined nature of this thesis, three special symmetric functions : elementary symmetric function , totally symmetric functions , powers and symmetric some combination of nature functions , and these were some of the nature of the application , as follows : The first chapter introduces the research object of this paper three : elementary symmetric function , totally symmetric functions and powers and symmetric functions . describes their definitions , the basic nature of the research situation , and finally gives their interpretation of a combination of the second chapter gives some three special properties of symmetric functions and the relationships between them , and got some containing binomial coefficients and two Stirling Number identities third chapter gives the elementary symmetric function matrix and completely symmetric function matrix decomposition , as the application has been Vandermonde matrix and its inverse matrix decomposition , and finally discuss the Vandermonde matrix of a matrix and its transpose relationship .