Bugfix: include empty combination #129
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This is a julia port of the sage VectorPartitions function originally written by Amritanshu Prasad (2013).
A vector partition of "vec" is a list of vectors with non-negative integer entries whose sum is "vec". The method vector_partitions creates all vector partitions of "vector" with all parts greater than or equal to "min" in lexicographic order recursively.
INPUT:
- "vec" -- a list of non-negative integers.
EXAMPLES:
If "min" is not specified, then the class of all vector partitions of
"vec" is created::
julia> vector_partitions([2, 2])
9-element Array{Any,1}:
Array{Int64,1}[[1,0],[1,0],[0,1],[0,1]]
Array{Int64,1}[[2,0],[0,1],[0,1]]
Array{Int64,1}[[1,1],[1,0],[0,1]]
Array{Int64,1}[[2,1],[0,1]]
Array{Int64,1}[[1,0],[1,0],[0,2]]
Array{Int64,1}[[2,0],[0,2]]
Array{Int64,1}[[1,2],[1,0]]
Array{Int64,1}[[1,1],[1,1]]
Array{Int64,1}[[2,2]]
Add vector_partitions.jl method
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Closes Issues #86 and #123. Currently the output of
combinations(a)does not include the empty combination, which is a bug. Also in the tests, we should havecombinations([]) = [[]], i.e., an array that contains the empty set, not the empty set itself.