1 | initial version |

It is not usual to bundle a database of combinatorial objects coming with Sage by default.

It would be nice to have a (fast) enumerated set of all lattices on a given number of elements. Although my impression is that the set of lattices on a given number of vertices is not easy to generate recursively. Indeed, the lattice property of a poset does not behave well with respect to inclusion, so a recursive enumeration would not work as smoothly as it does for posets.

That said, depending on what you want to do, you could use an iterator:

```
n_elmt=7
connected_lattice_iterator = (p for p in Posets(n_elmt) if p.is_connected() and p.is_lattice())
```

to generate all connected lattices one by one.

2 | No.2 Revision |

It is not usual to bundle a database of combinatorial objects coming with Sage by default.

It would be nice to have a (fast) enumerated set of all lattices on a given number of elements. Although my impression is that the set of lattices on a given number of vertices is not easy to generate recursively. Indeed, the lattice property of a poset does not behave well with respect to inclusion, so a recursive enumeration would not work as smoothly as it does for posets.

That said, depending on what you want to do, you could use an iterator:

~~n_elmt=7
~~n_elmt = 7
connected_lattice_iterator = (p for p in Posets(n_elmt) if p.is_connected() and p.is_lattice())

to generate all connected lattices one by one.

3 | No.3 Revision |

It is not usual to bundle a database of combinatorial objects coming with Sage by default.

It would be nice to have a (fast) enumerated set of all lattices on a given number of elements. Although my impression is that the set of lattices on a given number of vertices is not easy to generate recursively. Indeed, the lattice property of a poset does not behave well with respect to inclusion, so a recursive enumeration would not work as smoothly as it does for posets.

That said, depending on what you want to do, you could use an iterator:

```
n_elmt = 7
connected_lattice_iterator = (p for p in Posets(n_elmt) if p.is_connected() and p.is_lattice())
```

to generate all connected lattices one by ~~one.~~one, but it does not increase the speed of generation...

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.