code sage

Sage

There is a sage worksheet "RookTheoryGLnFq.sws" with almost all the examples and conjectures of the paper Rook Theory of the finite general linear group, arXiv:1707.08192. This worksheet contains an implementation of the recursive algorithm to compute the number of rank r matrices over a finite field F_q with support in the complement of the diagram of a permutation w. (added 11/01/2017)

• getMcW(w,r) which computes the number of rank r matrices with support in the complement of the diagram of the permutation w divided by (q-1)^r.

There is a sage worksheet "Combinatorics_Diagrams_Permutations.sws" with almost all the examples and figures of the paper Combinatorics of diagrams of permutations, arXiv:1405.1608

There is a sage worksheet "tourTablier.sws" with code for rook placements and diagrams.

The text file  "poincare.txt" has the following functions:

• invpoly(w) which computes the Poincare polynomial of a permutation w i.e., the rank generating function of the interval [id,w] in the strong Bruhat order of Sn,  

• ginvpoly(w) which computes the rank generating function of [w,w0].

The text file "pattavoidprocs.txt" has the functions:

• getPAPerms(n,plist) which gives a list of permutations in S_n that AVOID the patterns in plist

• getPAPerms2(Ps,plist) which gives a list of permutations in Ps that AVOID the patterns in plist

• getCPerms(n,plist) which gives a list of permutations in S_n that CONTAIN a pattern in plist

• getCPerms2(Ps,plist)  which gives a list of permutations in Ps that CONTAIN a pattern in plist

There is also a sage worksheet "poincarepattavoid.sws" with these functions and examples.