Littlewood-Richardson Calculator

The Littlewood-Richardson Calculator is a program designed to compute Littlewood-Richardson coefficients. This program is written in the C language to make the computation as efficient as possible. The program can compute single Littlewood-Richardson coefficients, products of Schur functions, or skew Schur functions. In addition it can compute products in the small quantum cohomology ring of a Grassmann variety. The software package also includes a program that performs fast computation of the more general multiplicative structure constants of Schubert polynomials.

The Littlewood-Richardson calculator has been integrated in the Sage Mathematics Software System. You may prefer to use the Littlewood-Richardson Calculator in this way to take advantage of the additional functions in Sage. The program is also available throught the package managers in several Linux distributions. For example, on Debian/Ubuntu it can be installed with the following command:

    % sudo apt install lrcalc

The Littlewood-Richardson Calculator has Python and Maple interfaces which are included in the software package distributed here. The Maple interface uses the same notation as the SF package of John Stembridge, to make it easier to use both packages at the same time.

The Littlewood-Richardson Calculator is open source software (under the GNU General Public License). To install it from source code, download the file

    lrcalc-2.1.tar.gz

and unpack it using the (unix) command:

    % tar zxvf lrcalc-2.1.tar.gz

This will create a directory named lrcalc-2.1. Now change to this directory and run the following commands:

    % cd lrcalc-2.1
    % ./configure
    % make
    % sudo make install

This will install the programs lrcalc and schubmult in the directory /usr/local/bin.

Please refer to the README file in the lrcalc-2.1 directory for more details, and see the ChangeLog file for a list of bug fixes, enhancements, and contributors. Special thanks go to Nicolas Thiery and Jean-Pierre Flori for adding the GNU automake system to the software package. Extra special thanks to Pierre-Emmanuel Chaput for suggestions that led to a large speedup in the computation of single LR coefficients.

People interested in writing enhancements to the software may wish to download it from the source repository, which is done with the following command:

    % git clone https://asbuch@bitbucket.org/asbuch/lrcalc.git

I will be grateful for any comments or bug reports for this package. Enjoy!

Anders Buch


During the development of this software, the author was partially supported by NSF grants DMS-0070479, DMS-0603822, DMS-0906148, and DMS-1205351.