- FindStat

Identifier

Mp00193: Lattices —to poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000327: Posets ⟶ ℤ

Values

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

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{1} = q$

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

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

Description

The number of cover relations in a poset.
Equivalently, this is also the number of edges in the Hasse diagram [1].

Map

order ideals

Description

The lattice of order ideals of a poset.
An order ideal

$\mathcal I$ in a poset

$P$ is a downward closed set, i.e.,

$a \in \mathcal I$ and

$b \leq a$ implies

$b \in \mathcal I$ . This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.

Map

to poset

Description

Return the poset corresponding to the lattice.