# Transition Matrices between Symmetric Polynomials

Version 1.0.6 (115 KB) by
A set of Matlab programs that computes the transition matrix between different bases of symmetric polynomials
Updated 31 Oct 2023

This Matlab program produces the transition matrix between six different bases of symmetric polynomials. The six bases are
e: elementary symmetric function
h: complete homogeneous symmetric function
m: monomial symmetric function
f: forgotten symmetric function
s: Schur function
p: power-sum symmetric function
Syntax:
M = trans_matrixd(k,b1,b2)
Input:
k: order of symmetric polynomials
b1: base 1
b2: base 2
bases 1 and 2 are either 'e', 'h', 'm', 'f', 's' or 'p'
Output
M: transition matrix that expresses symmetric polynomials in base 1 in terms of linear combination of symmetric polynomials in base 2.
M1: When the transition matrix consists of rational numbers (i.e., base 2 is p), we can specifiy two output arguments. In that case, both M and M1 are int64 matrices, and the transition matrix can be computed by using sym(M)./sym(M1)
Read manual.pdf for more information. I also had written a program to compute transition matrix between Jack polynomials and other symmetric polynomials. E-mail me if you need that.

### Cite As

Raymond Kan (2024). Transition Matrices between Symmetric Polynomials (https://www.mathworks.com/matlabcentral/fileexchange/136299-transition-matrices-between-symmetric-polynomials), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2023b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.0.6

Update the program for inverse Kostka matrix

1.0.5

Minor improvement on the program for computeing inverse Kostka matrix.

1.0.4

Updated inverse Kostka program

1.0.3

Improve efficiency of the symbolic version.

1.0.2

Fix a typo in the description

1.0.1

Update typo in the description.

1.0.0