- FindStat

Identifier

Mp00263: Lattices —join irreducibles⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
St001964: Posets ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

([(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) => ([],6) => ([],6) => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.

Map

dual poset

Description

The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.

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join irreducibles

Description

The poset of join irreducibles of a lattice.