# Affine Vector Space Partitions

Here I provide links to most of my collection of small affine vector space partitions (AVSPSs) in my Dropbox folder. This complements this preprint with John Bamberg, Yuval Filmus, and Sascha Kurz. The format is described below.

## AVSPs

### Classifications

1. AG(3, 2), 1 partitions.
2. AG(3, 3), 2 partitions.
3. AG(4, 2), 9 partitions.
4. AG(5, 2), 1050 partitions, up to size 9 and type 4^2 2^8, 212K.
5. AG(6, 2), 4 partitions, up to size 8.

1. AG(6, 2), 1 example.
2. AG(6, 3), 1 example.
3. AG(6, 4), 3 examples.
4. AG(6, 5), 1 example.
5. AG(6, 8), 1 example.

## File Format

The file format is as follows (for now my description is in Perl-style regular expressions):

1. Ignore everything till a row matches `/^n=([0-9])^+/`. Put n=\$1.
2. Ignore everything till a row matches `/^q=([0-9])^+/`. Put q=\$1.
3. Ignore everything till a row matches `/^T=[0-9]^+/`. Put T equal to the array `/([0-9]^+)/g` for that row.
4. Now follows an avsp in AG(n-1, q) with parts of size T, T, ..., T[\$#T]. Ignore everything except for characters in the alphabet A = [0-9a-zA-Z]. Let alpha be a primitive element of GF(q). Then we read 0 as 0 in GF(q) and any other element beta of A as alpha^beta. Here we read a=10, b=11, ..., Z=61. (No field sizes larger than 61 are supported.) T consists of the first T*n elements of A: The first n elements are the first basis vector of T, the next n are the second basis vector, and so on.
5. After all T[i]'s are read, repeat (or stop if the file ends).

Here is an example describing the unique partion of type 2^4 in AG(3, 2). We can use anything as delmiters in row 3. The commas and line breaks from line 4 to 7 are optional.

\$ cat avsps_n_4_q_2 n=4 q=2 T=2,2,2,2, 1000,0100, 1010,0001, 1001,0110, 1101,0011,

Here is an example describing the two partions of type 2^4 in AG(3, 3).

\$ cat avsps_n_4_q_3 n=4 q=3 T=2,2,2,2,2,2,2,2,2, 2000,0200, 2020,0002, 2010,0202, 2002,0220, 2202,0022, 2012,0222, 2001,0210, 2101,0021, 2011,0212, n=4 q=3 T=2,2,2,2,2,2,2,2,2, 2000,0200, 2020,0002, 2010,0202, 2002,0220, 2202,0021, 2102,0022, 2012,0222, 2001,0212, 2011,0210,