- FindStat

Identifier

Mp00262: Binary words —poset of factors⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001707: Graphs ⟶ ℤ

Values

=> ([(0,1)],2) => ([(0,1)],2) => 2
=> ([(0,1)],2) => ([(0,1)],2) => 2
=> ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => 3
=> ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
=> ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
=> ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => 3
=> ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4) => 4
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 6
=> ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 6
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 6
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 6
=> ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 6
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 6
=> ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4) => 4
=> ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 5
=> ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 5
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 6
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 6
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 7
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 7

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

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

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

Description

The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them.
Such a partition always exists because of a construction due to Dudek and Pralat [1] and independently Pokrovskiy [2].

Map

to graph

Description

Returns the Hasse diagram of the poset as an undirected graph.

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

$v$ .