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.
This Schur function can be written in terms of monomials by using
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 (); 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:
(%o1) true (%i2)