Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001767
(load all 2 compositions to match this statistic)
Mapping
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
St001767: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[-1] => [1]
 => [1]
 => 0
[1,-2] => [1]
 => [1]
 => 0
[-1,2] => [1]
 => [1]
 => 0
[-1,-2] => [1,1]
 => [2]
 => 1
[2,-1] => [2]
 => [1,1]
 => 1
[-2,1] => [2]
 => [1,1]
 => 1
[1,2,-3] => [1]
 => [1]
 => 0
[1,-2,3] => [1]
 => [1]
 => 0
[1,-2,-3] => [1,1]
 => [2]
 => 1
[-1,2,3] => [1]
 => [1]
 => 0
[-1,2,-3] => [1,1]
 => [2]
 => 1
[-1,-2,3] => [1,1]
 => [2]
 => 1
[-1,-2,-3] => [1,1,1]
 => [2,1]
 => 0
[1,3,-2] => [2]
 => [1,1]
 => 1
[1,-3,2] => [2]
 => [1,1]
 => 1
[-1,3,2] => [1]
 => [1]
 => 0
[-1,3,-2] => [2,1]
 => [3]
 => 1
[-1,-3,2] => [2,1]
 => [3]
 => 1
[-1,-3,-2] => [1]
 => [1]
 => 0
[2,1,-3] => [1]
 => [1]
 => 0
[2,-1,3] => [2]
 => [1,1]
 => 1
[2,-1,-3] => [2,1]
 => [3]
 => 1
[-2,1,3] => [2]
 => [1,1]
 => 1
[-2,1,-3] => [2,1]
 => [3]
 => 1
[-2,-1,-3] => [1]
 => [1]
 => 0
[2,3,-1] => [3]
 => [1,1,1]
 => 1
[2,-3,1] => [3]
 => [1,1,1]
 => 1
[-2,3,1] => [3]
 => [1,1,1]
 => 1
[-2,-3,-1] => [3]
 => [1,1,1]
 => 1
[3,1,-2] => [3]
 => [1,1,1]
 => 1
[3,-1,2] => [3]
 => [1,1,1]
 => 1
[-3,1,2] => [3]
 => [1,1,1]
 => 1
[-3,-1,-2] => [3]
 => [1,1,1]
 => 1
[3,2,-1] => [2]
 => [1,1]
 => 1
[3,-2,1] => [1]
 => [1]
 => 0
[3,-2,-1] => [2,1]
 => [3]
 => 1
[-3,2,1] => [2]
 => [1,1]
 => 1
[-3,-2,1] => [2,1]
 => [3]
 => 1
[-3,-2,-1] => [1]
 => [1]
 => 0
[1,2,3,-4] => [1]
 => [1]
 => 0
[1,2,-3,4] => [1]
 => [1]
 => 0
[1,2,-3,-4] => [1,1]
 => [2]
 => 1
[1,-2,3,4] => [1]
 => [1]
 => 0
[1,-2,3,-4] => [1,1]
 => [2]
 => 1
[1,-2,-3,4] => [1,1]
 => [2]
 => 1
[1,-2,-3,-4] => [1,1,1]
 => [2,1]
 => 0
[-1,2,3,4] => [1]
 => [1]
 => 0
[-1,2,3,-4] => [1,1]
 => [2]
 => 1
[-1,2,-3,4] => [1,1]
 => [2]
 => 1
[-1,2,-3,-4] => [1,1,1]
 => [2,1]
 => 0
Description
The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. Assign to each cell of the Ferrers diagram an arrow pointing north, east, south or west. Then compute for each cell the number of arrows pointing towards it, and take the minimum of those. This statistic is the maximal minimum that can be obtained by assigning arrows in any way.
Matching statistic: St000782
Mapping
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
St000782: Perfect matchings ⟶ ℤResult quality: 20% ●values known / values provided: 21%●distinct values known / distinct values provided: 20%
Values
[-1] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,-2] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,2] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,-2] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[2,-1] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[-2,1] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[1,2,-3] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,-2,3] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,-2,-3] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[-1,2,3] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,2,-3] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[-1,-2,3] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[-1,-2,-3] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [(1,2),(3,8),(4,7),(5,6)]
 => ? = 0
[1,3,-2] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[1,-3,2] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[-1,3,2] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,3,-2] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-1,-3,2] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-1,-3,-2] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[2,1,-3] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[2,-1,3] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[2,-1,-3] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-2,1,3] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[-2,1,-3] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-2,-1,-3] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[2,3,-1] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[2,-3,1] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[-2,3,1] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[-2,-3,-1] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[3,1,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[3,-1,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[-3,1,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[-3,-1,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[3,2,-1] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[3,-2,1] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[3,-2,-1] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-3,2,1] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[-3,-2,1] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-3,-2,-1] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,2,3,-4] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,2,-3,4] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,2,-3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[1,-2,3,4] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,-2,3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[1,-2,-3,4] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[1,-2,-3,-4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [(1,2),(3,8),(4,7),(5,6)]
 => ? = 0
[-1,2,3,4] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,2,3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[-1,2,-3,4] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[-1,2,-3,-4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [(1,2),(3,8),(4,7),(5,6)]
 => ? = 0
[-1,-2,3,4] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[-1,-2,3,-4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [(1,2),(3,8),(4,7),(5,6)]
 => ? = 0
[-1,-2,-3,4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [(1,2),(3,8),(4,7),(5,6)]
 => ? = 0
[-1,-2,-3,-4] => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [(1,2),(3,10),(4,9),(5,8),(6,7)]
 => ? = 1
[1,2,4,-3] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[1,2,-4,3] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[1,-2,4,3] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,-2,4,-3] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[1,-2,-4,3] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[1,-2,-4,-3] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,2,4,3] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,2,4,-3] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-1,2,-4,3] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-1,2,-4,-3] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,-2,4,3] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[-1,-2,4,-3] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [(1,2),(3,8),(4,5),(6,7)]
 => ? = 1
[-1,-2,-4,3] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [(1,2),(3,8),(4,5),(6,7)]
 => ? = 1
[-1,-2,-4,-3] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[1,3,2,-4] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,3,-2,4] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[1,3,-2,-4] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[1,-3,2,4] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[1,-3,2,-4] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[1,-3,-2,-4] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,3,2,4] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,3,2,-4] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[-1,3,-2,4] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-1,3,-2,-4] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [(1,2),(3,8),(4,5),(6,7)]
 => ? = 1
[-1,-3,2,4] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-1,-3,2,-4] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [(1,2),(3,8),(4,5),(6,7)]
 => ? = 1
[-1,-3,-2,4] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,-3,-2,-4] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[1,3,4,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[1,3,-4,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[1,-3,4,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[1,-3,-4,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => ? = 1
[-1,3,4,2] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[-1,3,4,-2] => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [(1,6),(2,3),(4,5),(7,8)]
 => ? = 1
[-1,3,-4,2] => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [(1,6),(2,3),(4,5),(7,8)]
 => ? = 1
[-1,3,-4,-2] => [1]
 => [1,0,1,0]
 => [(1,2),(3,4)]
 => ? = 0
[1,4,3,-2] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[1,4,-3,-2] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[1,-4,3,2] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
[1,-4,-3,2] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-1,4,3,-2] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-1,4,-3,2] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[-1,-4,3,2] => [2,1]
 => [1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => 1
[-1,-4,-3,-2] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[2,1,-3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => 1
[2,-1,3,4] => [2]
 => [1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => 1
Description
The indicator function of whether a given perfect matching is an L & P matching. An L&P matching is built inductively as follows: starting with either a single edge, or a hairpin $([1,3],[2,4])$, insert a noncrossing matching or inflate an edge by a ladder, that is, a number of nested edges. The number of L&P matchings is (see [thm. 1, 2]) $$\frac{1}{2} \cdot 4^{n} + \frac{1}{n + 1}{2 \, n \choose n} - {2 \, n + 1 \choose n} + {2 \, n - 1 \choose n - 1}$$
Matching statistic: St001491
Mapping
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 20%
Values
[-1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-2] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[2,-1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[-2,1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[1,2,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,-3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2,-3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,-2,3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,-2,-3] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 0
[1,3,-2] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[1,-3,2] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[-1,3,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,3,-2] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[-1,-3,2] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[-1,-3,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,1,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,-1,3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[2,-1,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[-2,1,3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[-2,1,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[-2,-1,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,3,-1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[2,-3,1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[-2,3,1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[-2,-3,-1] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[3,1,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[3,-1,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[-3,1,2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[-3,-1,-2] => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => ? = 1
[3,2,-1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[3,-2,1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[3,-2,-1] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[-3,2,1] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[-3,-2,1] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[-3,-2,-1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,2,3,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,2,-3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,2,-3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[1,-2,3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[1,-2,-3,4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[1,-2,-3,-4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 0
[-1,2,3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2,3,-4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,2,-3,4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,2,-3,-4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 0
[-1,-2,3,4] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,-2,3,-4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 0
[-1,-2,-3,4] => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => ? = 0
[-1,-2,-3,-4] => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1011110000 => ? = 1
[1,2,4,-3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[1,2,-4,3] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[1,-2,4,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,4,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[1,-2,-4,3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[1,-2,-4,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2,4,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,2,4,-3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[-1,2,-4,3] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[-1,2,-4,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-2,4,3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[-1,-2,4,-3] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 1
[-1,-2,-4,3] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 1
[-1,-2,-4,-3] => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 1
[1,3,2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,3,-2,4] => [2]
 => [1,1,0,0,1,0]
 => 110010 => ? = 1
[1,3,-2,-4] => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => ? = 1
[1,-3,-2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,3,2,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-3,-2,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,3,4,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,3,-4,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-3,4,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-3,-4,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,4,2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,4,-2,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-4,2,-3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-4,-2,3] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,4,-3,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[1,-4,-3,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,4,3,2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-1,-4,3,-2] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,1,3,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,1,-3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,-1,3,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,-1,-3,4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,3,1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,-3,-1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,3,-1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,-3,1,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,4,-3,1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[2,-4,-3,-1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,4,-3,-1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[-2,-4,-3,1] => [1]
 => [1,0,1,0]
 => 1010 => 0
[3,1,2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
[3,-1,-2,-4] => [1]
 => [1,0,1,0]
 => 1010 => 0
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let $A_n=K[x]/(x^n)$. We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.