- FindStat

Identifier

Mp00262: Binary words —poset of factors⟶ Posets
St000656: Posets ⟶ ℤ

Values

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

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

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

$F_{2} = 2\ q^{3} + 2\ q^{4}$

$F_{3} = 2\ q^{4} + 4\ q^{6} + 2\ q^{7}$

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

$A$ .

Map

poset of factors

Description

The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that

$u < v$ if and only if

$u$ is a factor of

$v$ .