Processing math: 100%

Identifier
Values
{{1}} => [1] => ([(0,1)],2) => ([(0,1)],2) => 1
{{1,2}} => [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
{{1},{2}} => [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
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
Description
The maximum magnitude of the Möbius function of a poset.
The Möbius function of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value μ(x,y) is equal to the signed sum of chains from x to y, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.
Map
lattice of intervals
Description
The lattice of intervals of a permutation.
An interval of a permutation π is a possibly empty interval of values that appear in consecutive positions of π. The lattice of intervals of π has as elements the intervals of π, ordered by set inclusion.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
to poset
Description
Return the poset corresponding to the lattice.