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D.15.8.4 LRmult
Procedure from library lrcalc.lib (see lrcalc_lib).
- Usage:
- LRmult(x, y); x, y lists of integers (partitions)
LRmult(x, y [, s, r]); x, y lists of integers (partitions),
s string equal to 'r', r integer
LRmult(x, y [, s, m, k]); x, y lists of integers (partitions),
s string equal to 'q' or 'f', m, k integers
- Return:
- list of lists
- Purpose:
- computes the partitions z for which the Littlewood-Richardson
coefficient c^z_{x,y} is non-zero together with that coefficient;
partitions up to length r
- Note:
Example:
| | LIB "lrcalc.lib";
// Compute the partitions z for which the Littlewood-Richardson coefficient
// c^z_{x,y} is non-zero together with that coefficient
// for x= (2, 1), y=(2, 1)
list x = 2, 1;
list y = 2, 1;
LRmult(x, y);
==> [1]:
==> [1]:
==> 2
==> [2]:
==> [1]:
==> 3
==> [2]:
==> 2
==> [3]:
==> 1
==> [2]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 4
==> [2]:
==> 2
==> [3]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 3
==> [2]:
==> 1
==> [3]:
==> 1
==> [4]:
==> 1
==> [4]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 3
==> [2]:
==> 3
==> [5]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 2
==> [2]:
==> 2
==> [3]:
==> 1
==> [4]:
==> 1
==> [6]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 2
==> [2]:
==> 2
==> [3]:
==> 2
==> [7]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 4
==> [2]:
==> 1
==> [3]:
==> 1
// Now compute only the partitions with at most 2 entries
LRmult(x, y, "r", 2);
==> [1]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 3
==> [2]:
==> 3
==> [2]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 4
==> [2]:
==> 2
// Now compute the product in the quantum cohomology ring of the Grassmannian Gr(3,3+2).
LRmult(x, y, "q", 3, 2);
==> [1]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 2
==> [2]:
==> 2
==> [3]:
==> 2
==> [2]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 1
// Compute the same product with the output given in fusion ring notation
LRmult(x, y, "f", 3, 2);
==> [1]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 2
==> [2]:
==> 2
==> [3]:
==> 2
==> [2]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> 3
==> [2]:
==> 2
==> [3]:
==> 1
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