Bugfix: let integer_partitions(0) == [Int[]] (#179)

* Fix `integer_partitions(0)`

* test: add length tests for `integer_partitions`

Author: inkydragon

src/partitions.jl

@@ -646,7 +646,7 @@ function integer_partitions(n::Integer)
     if n < 0
         throw(DomainError(n, "n must be nonnegative"))
     elseif n == 0
-        return Vector{Int}[]
+        return Vector{Int}[[]]
     elseif n == 1
         return Vector{Int}[[1]]
     end

test/partitions.jl

@@ -96,7 +96,7 @@
     end
 
     @testset "integer partitions" begin
-        @test_broken integer_partitions(0) == [[]]
+        @test integer_partitions(0) == [Int[]]
         @test integer_partitions(1) == [[1]]
         @test integer_partitions(2) == [[1, 1], [2]]
         @test integer_partitions(3) == [[1, 1, 1], [2, 1], [3]]
@@ -113,6 +113,16 @@
         # integer_partitions <--> partitions(::Integer)
         @test Set(integer_partitions(5)) == Set(partitions(5))
 
+        # Partition function p(n):  https://oeis.org/A000041
+        @test length(integer_partitions(0)) == 1
+        @test length(integer_partitions(1)) == 1
+        @test length(integer_partitions(2)) == 2
+        @test length(integer_partitions(3)) == 3
+        @test length(integer_partitions(4)) == 5
+        @test length(integer_partitions(5)) == 7
+        @test length(integer_partitions(40)) == 37338
+        @test length(integer_partitions(49)) == 173525
+
         @test_throws DomainError integer_partitions(-1)
     end