Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001243
Mapping
St001243: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => 1
[1,0,1,0]
 => 2
[1,1,0,0]
 => 3
[1,0,1,0,1,0]
 => 4
[1,0,1,1,0,0]
 => 6
[1,1,0,0,1,0]
 => 6
[1,1,0,1,0,0]
 => 9
[1,1,1,0,0,0]
 => 15
[1,0,1,0,1,0,1,0]
 => 10
[1,0,1,0,1,1,0,0]
 => 15
[1,0,1,1,0,0,1,0]
 => 15
[1,0,1,1,0,1,0,0]
 => 22
[1,0,1,1,1,0,0,0]
 => 36
[1,1,0,0,1,0,1,0]
 => 15
[1,1,0,0,1,1,0,0]
 => 23
[1,1,0,1,0,0,1,0]
 => 22
[1,1,0,1,0,1,0,0]
 => 33
[1,1,0,1,1,0,0,0]
 => 53
[1,1,1,0,0,0,1,0]
 => 36
[1,1,1,0,0,1,0,0]
 => 53
[1,1,1,0,1,0,0,0]
 => 87
[1,1,1,1,0,0,0,0]
 => 155
[1,0,1,0,1,0,1,0,1,0]
 => 26
[1,0,1,0,1,0,1,1,0,0]
 => 39
[1,0,1,0,1,1,0,0,1,0]
 => 39
[1,0,1,0,1,1,0,1,0,0]
 => 57
[1,0,1,0,1,1,1,0,0,0]
 => 93
[1,0,1,1,0,0,1,0,1,0]
 => 39
[1,0,1,1,0,0,1,1,0,0]
 => 59
[1,0,1,1,0,1,0,0,1,0]
 => 57
[1,0,1,1,0,1,0,1,0,0]
 => 84
[1,0,1,1,0,1,1,0,0,0]
 => 134
[1,0,1,1,1,0,0,0,1,0]
 => 93
[1,0,1,1,1,0,0,1,0,0]
 => 134
[1,0,1,1,1,0,1,0,0,0]
 => 216
[1,0,1,1,1,1,0,0,0,0]
 => 380
[1,1,0,0,1,0,1,0,1,0]
 => 39
[1,1,0,0,1,0,1,1,0,0]
 => 59
[1,1,0,0,1,1,0,0,1,0]
 => 59
[1,1,0,0,1,1,0,1,0,0]
 => 87
[1,1,0,0,1,1,1,0,0,0]
 => 143
[1,1,0,1,0,0,1,0,1,0]
 => 57
[1,1,0,1,0,0,1,1,0,0]
 => 87
[1,1,0,1,0,1,0,0,1,0]
 => 84
[1,1,0,1,0,1,0,1,0,0]
 => 125
[1,1,0,1,0,1,1,0,0,0]
 => 201
[1,1,0,1,1,0,0,0,1,0]
 => 134
[1,1,0,1,1,0,0,1,0,0]
 => 195
[1,1,0,1,1,0,1,0,0,0]
 => 317
[1,1,0,1,1,1,0,0,0,0]
 => 549
Description
The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. In other words, given a Dyck path, there is an associated (directed) unit interval graph $\Gamma$. Consider the expansion $$G_\Gamma(x;q) = \sum_{\kappa: V(G) \to \mathbb{N}_+} x_\kappa q^{\mathrm{asc}(\kappa)}$$ using the notation by Alexandersson and Panova. The function $G_\Gamma(x;q)$ is a so called unicellular LLT polynomial, and a symmetric function. Consider the Schur expansion $$G_\Gamma(x;q+1) = \sum_{\lambda} c^\Gamma_\lambda(q) s_\lambda(x).$$ By a result by Haiman and Grojnowski, all $c^\Gamma_\lambda(q)$ have non-negative integer coefficients. Consider the sum $$S_\Gamma = \sum_{\lambda} c^\Gamma_\lambda(1).$$ This statistic is $S_\Gamma$. It is still an open problem to find a combinatorial description of the above Schur expansion, a first step would be to find a family of combinatorial objects to sum over.
Matching statistic: St000034
(load all 2 compositions to match this statistic)
Mapping
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
St000034: Permutations ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 15%
Values
[1,0]
 => [(1,2)]
 => [2,1] => [2,1] => 0 = 1 - 1
[1,0,1,0]
 => [(1,2),(3,4)]
 => [2,1,4,3] => [4,2,1,3] => 1 = 2 - 1
[1,1,0,0]
 => [(1,4),(2,3)]
 => [4,3,2,1] => [4,3,2,1] => 2 = 3 - 1
[1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6)]
 => [2,1,4,3,6,5] => [6,4,2,1,3,5] => 3 = 4 - 1
[1,0,1,1,0,0]
 => [(1,2),(3,6),(4,5)]
 => [2,1,6,5,4,3] => [6,5,4,2,1,3] => ? ∊ {9,15} - 1
[1,1,0,0,1,0]
 => [(1,4),(2,3),(5,6)]
 => [4,3,2,1,6,5] => [6,4,3,2,1,5] => 5 = 6 - 1
[1,1,0,1,0,0]
 => [(1,6),(2,3),(4,5)]
 => [6,3,2,5,4,1] => [6,3,5,2,4,1] => 5 = 6 - 1
[1,1,1,0,0,0]
 => [(1,6),(2,5),(3,4)]
 => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ? ∊ {9,15} - 1
[1,0,1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6),(7,8)]
 => [2,1,4,3,6,5,8,7] => [8,6,4,2,1,3,5,7] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,0,1,0,1,1,0,0]
 => [(1,2),(3,4),(5,8),(6,7)]
 => [2,1,4,3,8,7,6,5] => [8,7,6,4,2,1,3,5] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,0,1,1,0,0,1,0]
 => [(1,2),(3,6),(4,5),(7,8)]
 => [2,1,6,5,4,3,8,7] => [8,6,5,4,2,1,3,7] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,0,1,1,0,1,0,0]
 => [(1,2),(3,8),(4,5),(6,7)]
 => [2,1,8,5,4,7,6,3] => [8,5,7,4,2,1,6,3] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,0,1,1,1,0,0,0]
 => [(1,2),(3,8),(4,7),(5,6)]
 => [2,1,8,7,6,5,4,3] => [8,7,6,5,4,2,1,3] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,1,0,0,1,0,1,0]
 => [(1,4),(2,3),(5,6),(7,8)]
 => [4,3,2,1,6,5,8,7] => [8,6,4,3,2,1,5,7] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,1,0,0,1,1,0,0]
 => [(1,4),(2,3),(5,8),(6,7)]
 => [4,3,2,1,8,7,6,5] => [8,7,6,4,3,2,1,5] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,1,0,1,0,0,1,0]
 => [(1,6),(2,3),(4,5),(7,8)]
 => [6,3,2,5,4,1,8,7] => [8,6,3,5,2,4,1,7] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,1,0,1,0,1,0,0]
 => [(1,8),(2,3),(4,5),(6,7)]
 => [8,3,2,5,4,7,6,1] => [8,3,7,5,2,4,6,1] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,1,0,1,1,0,0,0]
 => [(1,8),(2,3),(4,7),(5,6)]
 => [8,3,2,7,6,5,4,1] => [8,7,6,3,5,2,4,1] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,1,1,0,0,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8)]
 => [6,5,4,3,2,1,8,7] => [8,6,5,4,3,2,1,7] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,1,1,0,0,1,0,0]
 => [(1,8),(2,5),(3,4),(6,7)]
 => [8,5,4,3,2,7,6,1] => [8,5,7,4,3,2,6,1] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,1,1,0,1,0,0,0]
 => [(1,8),(2,7),(3,4),(5,6)]
 => [8,7,4,3,6,5,2,1] => [8,4,7,6,3,5,2,1] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,1,1,1,0,0,0,0]
 => [(1,8),(2,7),(3,6),(4,5)]
 => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => ? ∊ {10,15,15,15,22,22,23,33,36,36,53,53,87,155} - 1
[1,0,1,0,1,0,1,0,1,0]
 => [(1,2),(3,4),(5,6),(7,8),(9,10)]
 => [2,1,4,3,6,5,8,7,10,9] => [10,8,6,4,2,1,3,5,7,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,0,1,0,1,1,0,0]
 => [(1,2),(3,4),(5,6),(7,10),(8,9)]
 => [2,1,4,3,6,5,10,9,8,7] => [10,9,8,6,4,2,1,3,5,7] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,0,1,1,0,0,1,0]
 => [(1,2),(3,4),(5,8),(6,7),(9,10)]
 => [2,1,4,3,8,7,6,5,10,9] => [10,8,7,6,4,2,1,3,5,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,0,1,1,0,1,0,0]
 => [(1,2),(3,4),(5,10),(6,7),(8,9)]
 => [2,1,4,3,10,7,6,9,8,5] => [10,7,9,6,4,2,1,3,8,5] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,0,1,1,1,0,0,0]
 => [(1,2),(3,4),(5,10),(6,9),(7,8)]
 => [2,1,4,3,10,9,8,7,6,5] => [10,9,8,7,6,4,2,1,3,5] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,1,0,0,1,0,1,0]
 => [(1,2),(3,6),(4,5),(7,8),(9,10)]
 => [2,1,6,5,4,3,8,7,10,9] => [10,8,6,5,4,2,1,3,7,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,1,0,0,1,1,0,0]
 => [(1,2),(3,6),(4,5),(7,10),(8,9)]
 => [2,1,6,5,4,3,10,9,8,7] => [10,9,8,6,5,4,2,1,3,7] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,1,0,1,0,0,1,0]
 => [(1,2),(3,8),(4,5),(6,7),(9,10)]
 => [2,1,8,5,4,7,6,3,10,9] => [10,8,5,7,4,2,1,6,3,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,1,0,1,0,1,0,0]
 => [(1,2),(3,10),(4,5),(6,7),(8,9)]
 => [2,1,10,5,4,7,6,9,8,3] => [10,5,9,7,4,2,1,6,8,3] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,1,0,1,1,0,0,0]
 => [(1,2),(3,10),(4,5),(6,9),(7,8)]
 => [2,1,10,5,4,9,8,7,6,3] => [10,9,8,5,7,4,2,1,6,3] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,1,1,0,0,0,1,0]
 => [(1,2),(3,8),(4,7),(5,6),(9,10)]
 => [2,1,8,7,6,5,4,3,10,9] => [10,8,7,6,5,4,2,1,3,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,1,1,0,0,1,0,0]
 => [(1,2),(3,10),(4,7),(5,6),(8,9)]
 => [2,1,10,7,6,5,4,9,8,3] => [10,7,9,6,5,4,2,1,8,3] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,1,1,0,1,0,0,0]
 => [(1,2),(3,10),(4,9),(5,6),(7,8)]
 => [2,1,10,9,6,5,8,7,4,3] => [10,6,9,8,5,7,2,1,4,3] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,0,1,1,1,1,0,0,0,0]
 => [(1,2),(3,10),(4,9),(5,8),(6,7)]
 => [2,1,10,9,8,7,6,5,4,3] => [10,9,8,7,6,5,4,2,1,3] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,0,1,0,1,0,1,0]
 => [(1,4),(2,3),(5,6),(7,8),(9,10)]
 => [4,3,2,1,6,5,8,7,10,9] => [10,8,6,4,3,2,1,5,7,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,0,1,0,1,1,0,0]
 => [(1,4),(2,3),(5,6),(7,10),(8,9)]
 => [4,3,2,1,6,5,10,9,8,7] => [10,9,8,6,4,3,2,1,5,7] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,0,1,1,0,0,1,0]
 => [(1,4),(2,3),(5,8),(6,7),(9,10)]
 => [4,3,2,1,8,7,6,5,10,9] => [10,8,7,6,4,3,2,1,5,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,0,1,1,0,1,0,0]
 => [(1,4),(2,3),(5,10),(6,7),(8,9)]
 => [4,3,2,1,10,7,6,9,8,5] => [10,7,9,6,4,3,2,1,8,5] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,0,1,1,1,0,0,0]
 => [(1,4),(2,3),(5,10),(6,9),(7,8)]
 => [4,3,2,1,10,9,8,7,6,5] => [10,9,8,7,6,4,3,2,1,5] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,1,0,0,1,0,1,0]
 => [(1,6),(2,3),(4,5),(7,8),(9,10)]
 => [6,3,2,5,4,1,8,7,10,9] => [10,8,6,3,5,2,4,1,7,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,1,0,0,1,1,0,0]
 => [(1,6),(2,3),(4,5),(7,10),(8,9)]
 => [6,3,2,5,4,1,10,9,8,7] => [10,9,8,6,3,5,2,4,1,7] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,1,0,1,0,0,1,0]
 => [(1,8),(2,3),(4,5),(6,7),(9,10)]
 => [8,3,2,5,4,7,6,1,10,9] => [10,8,3,7,5,2,4,6,1,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,1,0,1,0,1,0,0]
 => [(1,10),(2,3),(4,5),(6,7),(8,9)]
 => [10,3,2,5,4,7,6,9,8,1] => [10,3,9,7,5,2,4,6,8,1] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,1,0,1,1,0,0,0]
 => [(1,10),(2,3),(4,5),(6,9),(7,8)]
 => [10,3,2,5,4,9,8,7,6,1] => [10,9,8,3,7,5,2,4,6,1] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,1,1,0,0,0,1,0]
 => [(1,8),(2,3),(4,7),(5,6),(9,10)]
 => [8,3,2,7,6,5,4,1,10,9] => [10,8,7,6,3,5,2,4,1,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,1,1,0,0,1,0,0]
 => [(1,10),(2,3),(4,7),(5,6),(8,9)]
 => [10,3,2,7,6,5,4,9,8,1] => [10,7,9,6,3,5,2,4,8,1] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,1,1,0,1,0,0,0]
 => [(1,10),(2,3),(4,9),(5,6),(7,8)]
 => [10,3,2,9,6,5,8,7,4,1] => [10,9,3,8,6,5,2,7,4,1] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,0,1,1,1,0,0,0,0]
 => [(1,10),(2,3),(4,9),(5,8),(6,7)]
 => [10,3,2,9,8,7,6,5,4,1] => [10,9,8,7,6,3,5,2,4,1] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,1,0,0,0,1,0,1,0]
 => [(1,6),(2,5),(3,4),(7,8),(9,10)]
 => [6,5,4,3,2,1,8,7,10,9] => [10,8,6,5,4,3,2,1,7,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,1,0,0,0,1,1,0,0]
 => [(1,6),(2,5),(3,4),(7,10),(8,9)]
 => [6,5,4,3,2,1,10,9,8,7] => [10,9,8,6,5,4,3,2,1,7] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,1,0,0,1,0,0,1,0]
 => [(1,8),(2,5),(3,4),(6,7),(9,10)]
 => [8,5,4,3,2,7,6,1,10,9] => [10,8,5,7,4,3,2,6,1,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,1,0,0,1,0,1,0,0]
 => [(1,10),(2,5),(3,4),(6,7),(8,9)]
 => [10,5,4,3,2,7,6,9,8,1] => [10,5,9,7,4,3,2,6,8,1] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,1,0,0,1,1,0,0,0]
 => [(1,10),(2,5),(3,4),(6,9),(7,8)]
 => [10,5,4,3,2,9,8,7,6,1] => [10,9,8,5,7,4,3,2,6,1] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
[1,1,1,0,1,0,0,0,1,0]
 => [(1,8),(2,7),(3,4),(5,6),(9,10)]
 => [8,7,4,3,6,5,2,1,10,9] => [10,8,4,7,6,3,5,2,1,9] => ? ∊ {26,39,39,39,39,57,57,57,59,59,59,84,84,87,87,93,93,93,125,134,134,134,134,143,143,195,201,201,216,216,317,317,317,380,380,507,549,549,887,887,1563,2915} - 1
Description
The maximum defect over any reduced expression for a permutation and any subexpression.