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Mon2schur Calculator

Mon2schur

Function: mon2schur (<L>) The list <L> represents the Schur function S_L: we have L = [i_1, i_2, ..., i_q], with i_1 <= i_2 <= ... <= i_q. The Schur function S_[i_1, i_2, ..., i_q] is the minor of the infinite matrix h_[i-j], i <= 1, j <= 1, consisting of the q first rows and the columns 1 + i_1, 2 + i_2, ..., q + i_q.

mon2schur ([1, 1, 1]);
 mon2schur ([3]);
 mon2schur ([1, 2]);

This Schur function can be written in terms of monomials by using treinat and kostka. The form returned is a symmetric polynomial in a contracted representation in the variables x_1,x_2,...

          (%i1) mon2schur ([1, 1, 1]);
          (%o1)                       x1 x2 x3
          (%i2) mon2schur ([3]);
                                            2        3
          (%o2)                x1 x2 x3 + x1  x2 + x1
          (%i3) mon2schur ([1, 2]);
                                                2
          (%o3)                  2 x1 x2 x3 + x1  x2

which means that for 3 variables this gives:

2 x1 x2 x3 + x1^2 x2 + x2^2 x1 + x1^2 x3 + x3^2 x1 + x2^2 x3 + x3^2 x2 Other functions for changing bases: comp2ele.

(%o1)                                true
(%i2) 

Mon2schur Example

Related Examples

mon2schur

mon2schur ([1, 1, 1]);

mon2schur ([3]);

mon2schur ([1, 2]);

Calculate

mon2schur

? mon2schur;

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mon2schur

mon2schur ([1, 1, 1]);

mon2schur ([3]);

mon2schur ([1, 2]);

Calculate

mon2schur

? mon2schur;

Calculate