Your data matches 21 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
St000518: Binary words ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => 2
1 => 2
00 => 3
01 => 4
10 => 4
11 => 3
000 => 4
001 => 6
010 => 7
011 => 6
100 => 6
101 => 7
110 => 6
111 => 4
Description
The number of distinct subsequences in a binary word. In contrast to the subword complexity [[St000294]] this is the cardinality of the set of all subsequences of not necessarily consecutive letters.
Matching statistic: St000656
Mp00262: Binary words poset of factorsPosets
St000656: Posets ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => ([(0,1)],2)
=> 2
1 => ([(0,1)],2)
=> 2
00 => ([(0,2),(2,1)],3)
=> 3
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
11 => ([(0,2),(2,1)],3)
=> 3
000 => ([(0,3),(2,1),(3,2)],4)
=> 4
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 7
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 7
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
111 => ([(0,3),(2,1),(3,2)],4)
=> 4
Description
The number of cuts of a poset. A cut is a subset $A$ of the poset such that the set of lower bounds of the set of upper bounds of $A$ is exactly $A$.
Mp00178: Binary words to compositionInteger compositions
Mp00184: Integer compositions to threshold graphGraphs
St000087: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => [2] => ([],2)
=> 2
1 => [1,1] => ([(0,1)],2)
=> 2
00 => [3] => ([],3)
=> 3
01 => [2,1] => ([(0,2),(1,2)],3)
=> 4
10 => [1,2] => ([(1,2)],3)
=> 4
11 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
000 => [4] => ([],4)
=> 4
001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 6
010 => [2,2] => ([(1,3),(2,3)],4)
=> 7
011 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
100 => [1,3] => ([(2,3)],4)
=> 6
101 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 7
110 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 6
111 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4
Description
The number of induced subgraphs. A subgraph $H \subseteq G$ is induced if $E(H)$ consists of all edges in $E(G)$ that connect the vertices of $H$.
Matching statistic: St000391
Mp00234: Binary words valleys-to-peaksBinary words
Mp00224: Binary words runsortBinary words
St000391: Binary words ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => 1 => 1 => 1 = 2 - 1
1 => 1 => 1 => 1 = 2 - 1
00 => 01 => 01 => 2 = 3 - 1
01 => 10 => 01 => 2 = 3 - 1
10 => 11 => 11 => 3 = 4 - 1
11 => 11 => 11 => 3 = 4 - 1
000 => 001 => 001 => 3 = 4 - 1
001 => 010 => 001 => 3 = 4 - 1
010 => 101 => 011 => 5 = 6 - 1
011 => 101 => 011 => 5 = 6 - 1
100 => 101 => 011 => 5 = 6 - 1
101 => 110 => 011 => 5 = 6 - 1
110 => 111 => 111 => 6 = 7 - 1
111 => 111 => 111 => 6 = 7 - 1
Description
The sum of the positions of the ones in a binary word.
Matching statistic: St001658
Mp00178: Binary words to compositionInteger compositions
Mp00180: Integer compositions to ribbonSkew partitions
St001658: Skew partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => [2] => [[2],[]]
=> 3 = 2 + 1
1 => [1,1] => [[1,1],[]]
=> 3 = 2 + 1
00 => [3] => [[3],[]]
=> 4 = 3 + 1
01 => [2,1] => [[2,2],[1]]
=> 5 = 4 + 1
10 => [1,2] => [[2,1],[]]
=> 5 = 4 + 1
11 => [1,1,1] => [[1,1,1],[]]
=> 4 = 3 + 1
000 => [4] => [[4],[]]
=> 5 = 4 + 1
001 => [3,1] => [[3,3],[2]]
=> 7 = 6 + 1
010 => [2,2] => [[3,2],[1]]
=> 8 = 7 + 1
011 => [2,1,1] => [[2,2,2],[1,1]]
=> 7 = 6 + 1
100 => [1,3] => [[3,1],[]]
=> 7 = 6 + 1
101 => [1,2,1] => [[2,2,1],[1]]
=> 8 = 7 + 1
110 => [1,1,2] => [[2,1,1],[]]
=> 7 = 6 + 1
111 => [1,1,1,1] => [[1,1,1,1],[]]
=> 5 = 4 + 1
Description
The total number of rook placements on a Ferrers board.
Matching statistic: St001259
Mp00097: Binary words delta morphismInteger compositions
Mp00231: Integer compositions bounce pathDyck paths
Mp00101: Dyck paths decomposition reverseDyck paths
St001259: Dyck paths ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => [1] => [1,0]
=> [1,0]
=> 2
1 => [1] => [1,0]
=> [1,0]
=> 2
00 => [2] => [1,1,0,0]
=> [1,0,1,0]
=> 4
01 => [1,1] => [1,0,1,0]
=> [1,1,0,0]
=> 3
10 => [1,1] => [1,0,1,0]
=> [1,1,0,0]
=> 3
11 => [2] => [1,1,0,0]
=> [1,0,1,0]
=> 4
000 => [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 6
001 => [2,1] => [1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> 7
010 => [1,1,1] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 4
011 => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 6
100 => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 6
101 => [1,1,1] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 4
110 => [2,1] => [1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> 7
111 => [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 6
Description
The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra.
Matching statistic: St001684
Mp00178: Binary words to compositionInteger compositions
Mp00231: Integer compositions bounce pathDyck paths
Mp00201: Dyck paths RingelPermutations
St001684: Permutations ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => [2] => [1,1,0,0]
=> [2,3,1] => 2
1 => [1,1] => [1,0,1,0]
=> [3,1,2] => 2
00 => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 3
01 => [2,1] => [1,1,0,0,1,0]
=> [2,4,1,3] => 4
10 => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 4
11 => [1,1,1] => [1,0,1,0,1,0]
=> [4,1,2,3] => 3
000 => [4] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 4
001 => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => 6
010 => [2,2] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => 7
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => 6
100 => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => 6
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => 7
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 6
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 4
Description
The reduced word complexity of a permutation. For a permutation $\pi$, this is the smallest length of a word in simple transpositions that contains all reduced expressions of $\pi$. For example, the permutation $[3,2,1] = (12)(23)(12) = (23)(12)(23)$ and the reduced word complexity is $4$ since the smallest words containing those two reduced words as subwords are $(12),(23),(12),(23)$ and also $(23),(12),(23),(12)$. This statistic appears in [1, Question 6.1].
Matching statistic: St000070
Mp00178: Binary words to compositionInteger compositions
Mp00180: Integer compositions to ribbonSkew partitions
Mp00185: Skew partitions cell posetPosets
St000070: Posets ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => [2] => [[2],[]]
=> ([(0,1)],2)
=> 3 = 2 + 1
1 => [1,1] => [[1,1],[]]
=> ([(0,1)],2)
=> 3 = 2 + 1
00 => [3] => [[3],[]]
=> ([(0,2),(2,1)],3)
=> 4 = 3 + 1
01 => [2,1] => [[2,2],[1]]
=> ([(0,2),(1,2)],3)
=> 5 = 4 + 1
10 => [1,2] => [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> 5 = 4 + 1
11 => [1,1,1] => [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 4 = 3 + 1
000 => [4] => [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 5 = 4 + 1
001 => [3,1] => [[3,3],[2]]
=> ([(0,3),(1,2),(2,3)],4)
=> 7 = 6 + 1
010 => [2,2] => [[3,2],[1]]
=> ([(0,3),(1,2),(1,3)],4)
=> 8 = 7 + 1
011 => [2,1,1] => [[2,2,2],[1,1]]
=> ([(0,3),(1,2),(2,3)],4)
=> 7 = 6 + 1
100 => [1,3] => [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> 7 = 6 + 1
101 => [1,2,1] => [[2,2,1],[1]]
=> ([(0,3),(1,2),(1,3)],4)
=> 8 = 7 + 1
110 => [1,1,2] => [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> 7 = 6 + 1
111 => [1,1,1,1] => [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 5 = 4 + 1
Description
The number of antichains in a poset. An antichain in a poset $P$ is a subset of elements of $P$ which are pairwise incomparable. An order ideal is a subset $I$ of $P$ such that $a\in I$ and $b \leq_P a$ implies $b \in I$. Since there is a one-to-one correspondence between antichains and order ideals, this statistic is also the number of order ideals in a poset.
Matching statistic: St000110
Mp00178: Binary words to compositionInteger compositions
Mp00231: Integer compositions bounce pathDyck paths
Mp00201: Dyck paths RingelPermutations
St000110: Permutations ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => [2] => [1,1,0,0]
=> [2,3,1] => 3 = 2 + 1
1 => [1,1] => [1,0,1,0]
=> [3,1,2] => 3 = 2 + 1
00 => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 4 = 3 + 1
01 => [2,1] => [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 4 + 1
10 => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 4 + 1
11 => [1,1,1] => [1,0,1,0,1,0]
=> [4,1,2,3] => 4 = 3 + 1
000 => [4] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 5 = 4 + 1
001 => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => 7 = 6 + 1
010 => [2,2] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => 8 = 7 + 1
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => 7 = 6 + 1
100 => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => 7 = 6 + 1
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => 8 = 7 + 1
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 7 = 6 + 1
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 5 = 4 + 1
Description
The number of permutations less than or equal to a permutation in left weak order. This is the same as the number of permutations less than or equal to the given permutation in right weak order.
Matching statistic: St001464
Mp00178: Binary words to compositionInteger compositions
Mp00231: Integer compositions bounce pathDyck paths
Mp00201: Dyck paths RingelPermutations
St001464: Permutations ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
0 => [2] => [1,1,0,0]
=> [2,3,1] => 3 = 2 + 1
1 => [1,1] => [1,0,1,0]
=> [3,1,2] => 3 = 2 + 1
00 => [3] => [1,1,1,0,0,0]
=> [2,3,4,1] => 4 = 3 + 1
01 => [2,1] => [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 4 + 1
10 => [1,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 4 + 1
11 => [1,1,1] => [1,0,1,0,1,0]
=> [4,1,2,3] => 4 = 3 + 1
000 => [4] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 5 = 4 + 1
001 => [3,1] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => 7 = 6 + 1
010 => [2,2] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => 8 = 7 + 1
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => 7 = 6 + 1
100 => [1,3] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => 7 = 6 + 1
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => 8 = 7 + 1
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 7 = 6 + 1
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 5 = 4 + 1
Description
The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise.
The following 11 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001812The biclique partition number of a graph. St001875The number of simple modules with projective dimension at most 1. St001645The pebbling number of a connected graph. St000422The energy of a graph, if it is integral. St001330The hat guessing number of a graph. St000454The largest eigenvalue of a graph if it is integral. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St000455The second largest eigenvalue of a graph if it is integral.