---
name: "lrcalc"
section: "1"
platform: "linux"
package: "lrcalc"
version: "1.2-2.2"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/lrcalc"
---

# lrcalc(1)

Calculate with Littlewood-Richardson coefficients

## NAME

lrcalc - Calculate with Littlewood-Richardson coefficients

## SYNOPSIS

**lrcalc** *coprod* \[**-a**\] *part*\
 **lrcalc** *lrcoef* *outer* **-** *inner1* **-** *inner2*\
 **lrcalc** *lrtab* \[**-r** *rows*\] *outer* **/** *inner*\
 **lrcalc** *mult* \[**-mz**\] \[**-r** *rows*\] \[**-q** *rows*,*cols*\] \[**-f** *rows*,*level*\] *part1* **-** *part2*\
 **lrcalc** *skew* \[**-m**\] \[**-r** *rows*\] *outer* **/** *inner*

## coprod - Calculate coproducts in the ring of symmetric functions

**DESCRIPTION**

The command "**lrcalc** *coprod* *z*" lists all pairs of partitions x and y for which the Littlewood-Richardson coefficient c^z\_{x,y} is non-zero, with that coefficient in front.

**OPTIONS**

- **-a**

  not documented

**EXAMPLE**

% lrcalc coprod 3 2 1\
 1  (3, 1)  (2)\
 1  (2, 2)  (1, 1)\
 1  (3, 1)  (1, 1)\
 1  (2, 1)  (3)\
 2  (2, 1)  (2, 1)\
 1  (2, 2, 1)  (1)\
 1  (3, 2, 1)  ()\
 1  (3, 2)  (1)\
 1  (2, 1, 1)  (2)\
 1  (3, 1, 1)  (1)\
 1  (1, 1, 1)  (2, 1)\
 1  (2, 1, 1)  (1, 1)\
 1  (2, 2)  (2)

## lrcoef - Compute a single Littlewood-Richardson coefficient

**DESCRIPTION**

The command "**lrcalc** *lrcoef* *z* **-** *x* **-** *y*" computes the Littlewood-Richardson coefficient c^z\_{x,y} which is the coefficient of the Schur function s\_z in the product s\_x \* s\_y.

**EXAMPLE**

% lrcalc lrcoef 3 2 1 - 2 1 - 2 1\
 2

## lrtab

not documented

## mult - Expand a product of two Schur functions in the basis of Schur functions

**DESCRIPTION**

The command "**lrcalc** *mult* *x* **-** *y*" lists all partitions z for which the Littlewood-Richardson coefficient c^z\_{x,y} is non-zero, with that coefficient in front.

**OPTIONS**

- **-mz**

  not documented

- **-r** *rows*

  not documented

- **-q** *rows*,*cols*

  Calculates quantum coefficients. Experimental feature.

- **-f** *rows*,*level*

  Calculates fusion coefficients. Experimental feature.

**EXAMPLES**

% lrcalc mult 2 1 - 2 1\
 1  (3, 3)\
 1  (4, 2)\
 1  (2, 2, 1, 1)\
 1  (2, 2, 2)\
 2  (3, 2, 1)\
 1  (4, 1, 1)\
 1  (3, 1, 1, 1)

% lrcalc mult -f 3,2 3 2 1 - 3 2 1\
 1  (4, 4, 4)\
 1  (5, 4, 3)

% lrcalc mult -q 3,2 3 2 1 - 3 2 1\
 1  (2)\
 1  (1, 1)

## skew - Expand a skew Schur function in the basis of Schur functions

**DESCRIPTION**

The command "**lrcalc** *skew* *z* **/** *x*" lists all partitions y for which the Littlewood-Richardson coefficient c^z\_{x,y} is non-zero, with that coefficient in front.

**OPTIONS**

- **-m**

  not documented

- **-r** *rows*

  not documented

**EXAMPLE**

% lrcalc skew 3 2 1 / 2 1\
 1  (3)\
 2  (2, 1)\
 1  (1, 1, 1)

## AUTHOR

Anders S. Buch \<asbuch at math rutgers edu\>

## MANPAGE AUTHOR

Tobias Hansen \<thansen at debian dot org\>