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D.15.7.3 LRskew

Procedure from library lrcalc.lib (see lrcalc_lib).

Usage:
LRskew(z, x [,s, r]); z, x lists of integers (partitions) s string equal to 'r', r non-negative integer

Return:
list of lists

Purpose:
computes the partitions y for which the Littlewood-Richardson coefficient c^z_{x,y} is non-zero together with that coefficient; only partitions up to length r are computed
if the optional parameters age given

Note:

Example:
 
LIB "lrcalc.lib";
// Compute the partitions y for which the Littlewood-Richardson coefficient
// c^z_{x,y} is non-zero together with that coefficient
// for z= (3, 2, 1), x=(2, 1)
list z = 3, 2, 1;
list x = 2, 1;
LRskew(z, x);
==> [1]:
==>    [1]:
==>       1
==>    [2]:
==>       [1]:
==>          3
==> [2]:
==>    [1]:
==>       2
==>    [2]:
==>       [1]:
==>          2
==>       [2]:
==>          1
==> [3]:
==>    [1]:
==>       1
==>    [2]:
==>       [1]:
==>          1
==>       [2]:
==>          1
==>       [3]:
==>          1
// Now compute only the partitions with at most 2 entries
LRskew(z, x, "r", 2);
==> [1]:
==>    [1]:
==>       1
==>    [2]:
==>       [1]:
==>          3
==> [2]:
==>    [1]:
==>       2
==>    [2]:
==>       [1]:
==>          2
==>       [2]:
==>          1