- FindStat

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Identifier

St001620: Lattices ⟶ ℤ

Values

([],1) => 2

([(0,1)],2) => 4

([(0,2),(2,1)],3) => 8

([(0,1),(0,2),(1,3),(2,3)],4) => 13

([(0,3),(2,1),(3,2)],4) => 16

([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 20

([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 23

([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 26

([(0,4),(2,3),(3,1),(4,2)],5) => 32

([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 26

([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 31

([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 34

([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 36

([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 40

([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 46

([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 52

([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 43

([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 52

([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 36

([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 52

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 40

([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 37

([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 38

([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 64

([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 46

([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 50

([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 53

([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 53

([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 55

([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 62

([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => 68

([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => 72

([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => 80

([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => 62

([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => 72

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 68

([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 104

([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => 74

([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 76

([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => 62

([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => 69

([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 80

([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 53

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => 69

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 85

([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 55

([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => 80

([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 62

([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => 56

([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 54

([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 104

([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 72

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => 55

([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 68

([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 56

([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 53

([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 62

([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 76

([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 69

([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 56

([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 55

([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 86

([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => 63

([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 92

([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => 72

([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 54

([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 62

([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 83

([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => 104

([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => 62

([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 92

([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 65

([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 92

([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 69

([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 128

([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => 74

([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 86

([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 104

([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 85

([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8) => 88

([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8) => 84

([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8) => 82

([(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4)],8) => 86

([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8) => 100

([(0,6),(1,7),(2,7),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5)],8) => 106

([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8) => 106

([(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(5,4),(7,6)],8) => 110

([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8) => 124

([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(6,1),(6,2),(6,5)],8) => 93

([(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8) => 106

([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,2),(5,3),(6,7)],8) => 96

([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8) => 103

([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8) => 160

([(0,5),(1,7),(2,6),(3,6),(4,1),(5,2),(5,3),(5,4),(6,7)],8) => 112

([(0,4),(1,6),(2,5),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8) => 108

([(0,5),(1,7),(2,7),(3,6),(4,3),(4,7),(5,1),(5,2),(5,4),(7,6)],8) => 110

([(0,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7),(7,1)],8) => 144

([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,4),(7,3)],8) => 138

([(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(6,1),(6,4),(6,5)],8) => 112

([(0,5),(1,7),(2,7),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4),(6,7)],8) => 106

([(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(6,1),(6,5)],8) => 91

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$F_{1} = q^{2}$

$F_{2} = q^{4}$

$F_{3} = q^{8}$

$F_{4} = q^{13} + q^{16}$

$F_{5} = q^{20} + q^{23} + 2\ q^{26} + q^{32}$

$F_{6} = q^{31} + q^{34} + 2\ q^{36} + q^{37} + q^{38} + 2\ q^{40} + q^{43} + 2\ q^{46} + 3\ q^{52} + q^{64}$

$F_{7} = q^{50} + 4\ q^{53} + 2\ q^{54} + 4\ q^{55} + 3\ q^{56} + 7\ q^{62} + q^{63} + q^{65} + 3\ q^{68} + 4\ q^{69} + 4\ q^{72} + 2\ q^{74} + 2\ q^{76} + 3\ q^{80} + q^{83} + q^{85} + 2\ q^{86} + 3\ q^{92} + 4\ q^{104} + q^{128}$

$F_{8} = q^{74} + 2\ q^{76} + 4\ q^{77} + 4\ q^{78} + q^{80} + 4\ q^{82} + q^{83} + 5\ q^{84} + 7\ q^{85} + 4\ q^{86} + 5\ q^{87} + q^{88} + 2\ q^{89} + 2\ q^{90} + 5\ q^{91} + 2\ q^{92} + 6\ q^{93} + 8\ q^{94} + 6\ q^{96} + 9\ q^{97} + 12\ q^{100} + 2\ q^{102} + 5\ q^{103} + q^{104} + 8\ q^{106} + 2\ q^{107} + 4\ q^{108} + q^{109} + 12\ q^{110} + 6\ q^{112} + 2\ q^{113} + 3\ q^{114} + 2\ q^{115} + 2\ q^{118} + 2\ q^{119} + 3\ q^{121} + 13\ q^{124} + q^{125} + 2\ q^{126} + 2\ q^{130} + 2\ q^{131} + 2\ q^{132} + 2\ q^{133} + 2\ q^{135} + 5\ q^{136} + 8\ q^{138} + 6\ q^{144} + 3\ q^{148} + 2\ q^{151} + 3\ q^{152} + 4\ q^{160} + q^{163} + 2\ q^{166} + q^{169} + 2\ q^{170} + 3\ q^{172} + 4\ q^{184} + 5\ q^{208} + q^{256}$

Description

The number of sublattices of a lattice.

Code

def statistic(L):
    return sum(1 for _ in L._hasse_diagram.sublattices_iterator(set(), 0))

Created

Sep 29, 2020 at 20:16 by Martin Rubey

Updated

Sep 29, 2020 at 20:16 by Martin Rubey