Processing math: 100%

Identifier
Values
0 => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
1 => ([(0,1)],2) => ([(0,2),(2,1)],3) => 1
00 => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
10 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
11 => ([(0,2),(2,1)],3) => ([(0,3),(2,1),(3,2)],4) => 1
000 => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
111 => ([(0,3),(2,1),(3,2)],4) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
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Description
The breadth of a lattice.
The breadth of a lattice is the least integer b such that any join x1x2xn, with n>b, can be expressed as a join over a proper subset of {x1,x2,,xn}.
Map
order ideals
Description
The lattice of order ideals of a poset.
An order ideal I in a poset P is a downward closed set, i.e., aI and ba implies bI. This map sends a poset to the lattice of all order ideals sorted by inclusion with meet being intersection and join being union.
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.