PermStruct is an algorithm for discovering descriptions of permutation sets in terms of so-called generating rules. These descriptions can then be used to derive generating functions for the permutation sets.

To install PermStruct on your system, start by installing the Permuta library. PermStruct was built on an older version of Permuta so you will need to swap to the branch called "struct". Then run the following commands:

$ sudo ./setup.py install

If you have Gurobi installed then you are done. If you do not have it run:

$ make -C exact_cover
$ sudo make -C exact_cover install

You can also possible to install PermStruct in development mode, in which case you run the following instead:

$ sudo ./setup.py develop

To run the unit tests, you can run the following command:

$ ./setup.py test

Once you've installed PermStruct, it can be imported into a Python script like any other Python library:

import permstruct

As an example we run the algorithm on permutations avoiding the pattern 231. We start by defining the basis patts and then run the algorithm.

patts = [Permutation([2,3,1])]
struct(patts)

When the input is just the basis the algorithm will infer other settings from the longest pattern in the basis, k = 3 here:

• size=k + 1 (the maximum size of the rules to try)
• perm_bound=max(size + 1, k + 2) (the longest permutations to use from Av(patts))
• verify_bound=perm_bound + 2 (the longest permutations from Av(patts) to use to verify the cover found)
• subpatts_len=None (the longest subpattern to use from the basis; None implies we use all subpatterns)
• subpatts_num=None (the maximum number of subpatterns to use from the basis)
• subpatts_type=SubPatternType.EVERY (the type of subpattern to use from the basis)
• ask_verify_higher=True (whether to ask about verifying with longer permutations)

If the algorithm is too slow it good to try to decrease the size of the rules (size). If the algorithm does not find a cover it is often good to try increasing the rule size. If the algorithm finds a cover that is not verified it is good to increase the perm_bound.

If you have PyPy installed you can do all of the above in PyPy.

BSD-3: see the LICENSE file.