Schur polynomials Access to and change of parts Building

Building

In order to build or to make a new SCHURobject we have the following routines (cf. also the corresponding routines for POLYNOMobjects) which differ in the handling of the various inputs: make does a copy and build does not copy. Sometimes you have a PARTITION and you want to build a SCHURobject out of it. This you can do as follows: Sometimes you even have a VECTORobject of INTEGERobject, which you want to sort to a PARTITIONobject, and then you want to build a SCHURobject out of it Sometimes you may want to know the common constituents (including their multiplicities) of two SCHURobjects (which are linear combinations of Schur polynomials), they can be evaluated using the following routine: The outer product of two Schur polynomials (= the linear combination, the coefficients of which obey the Littlewood-Richardson rule) is evaluated as follows: The symmetric part of a Schubert polynomial in terms of Schur polynomials: Expansion of Schur polynomials with prescribed alphabet:
Example:
...
scan(PARTITION,a);
scan(INTEGER,b);
compute_schur_with_alphabet(a,b,c);println(c);
...
Expansion of a complete symmetric function: Expansion of monomial symmetric functions:
Example:
...
scan(PARTITION,a); scan(INTEGER,b);
compute_monomial_with_alphabet(a,b,c); println(c);
...
Expansion of power sum symmetric functions: Another expansion of Schur polynomials: Expansion of skew Schur polynomials:
Example:
...
scan(SKEWPARTITION,a);
scan(INTEGER,b);
compute_skewschur_with_alphabet_det(a,b,d);println(d);
...
The evaluation of the Hall-Littlewood polynomials:
harald.fripertinger "at" uni-graz.at, May 26, 2011

Schur polynomials Access to and change of parts Uni-Graz Mathematik Building Valid HTML 4.0 Transitional Valid CSS!