Special gaussoids

This page provides lists of the special gaussoids in small dimension from Table 1 of Construction Methods for Gaussoids.

For each class of special gaussoids, we provide a verification of the count from Table 1 as well as a listing of all members for small dimensions. Some listings are bzip2-compressed and those inflate to between 3 and 6 GiB. The source CNF file is linked in the first column.

Download

DSHARP time nbc_minisat_all time
ELUBF3 11 0.00 cnf3-list.txt 0.00
ELUBF4 679 0.01 cnf4-list.txt 0.01
ELUBF5 60212776 81.38 cnf5-list.txt.bz2 1242
ELUB3 10 0.00 ELUB3-list.txt 0.00
ELUB4 640 0.01 ELUB4-list.txt 0.01
ELUB5 59348930 72.75 ELUB5-list.txt.bz2 1223
ELUF3 8 0.00 ELUF3-list.txt 0.00
ELUF4 522 0.00 ELUF4-list.txt 0.00
ELUF5 48633672 13.12 ELUF5-list.txt.bz2 1002
ELU3 7 0.00 ELU3-list.txt 0.00
ELU4 513 0.00 ELU4-list.txt 0.00
ELU5 47867881 10.39 ELU5-list.txt.bz2 984
LUB3 9 0.00 LUB3-list.txt 0.00
LUB4 111 0.01 LUB4-list.txt 0.00
LUB5 0 0.60 LUB5-list.txt 0.54
LUF3 7 0.00 LUF3-list.txt 0.00
LUF4 61 0.00 LUF4-list.txt 0.00
LUF5 1 0.06 LUF5-list.txt 0.10
LU3 6 0.00 LU3-list.txt 0.00
LU4 60 0.00 LU4-list.txt 0.00
LU5 0 0.05 LU5-list.txt 0.10
UB3 6 0.00 UB3-list.txt 0.00
UB4 15 0.00 UB4-list.txt 0.00
UB5 0 0.01 UB5-list.txt 0.00
UF3 4 0.00 UF3-list.txt 0.00
UF4 1 0.00 UF4-list.txt 0.00
UF5 1 0.00 UF5-list.txt 0.00
EF3 2 0.00 EF3-list.txt 0.00
EF4 2 0.00 EF4-list.txt 0.00
EF5 2 0.00 EF5-list.txt 0.00
EUBF3 8 0.00 EUBF3-list.txt 0.00
EUBF4 64 0.00 EUBF4-list.txt 0.00
EUBF5 1024 0.31 EUBF5-list.txt 0.11
EUBF6 32768 59.86 EUBF6-list.txt 8.28
EUB3 7 0.00 EUB3-list.txt 0.00
EUB4 41 0.00 EUB4-list.txt 0.00
EUB5 388 0.17 EUB5-list.txt 0.05
EUB6 5789 8.22 EUB6-list.txt 1.38
UBF3 7 0.00 UBF3-list.txt 0.00
UBF4 34 0.00 UBF4-list.txt 0.00
UBF5 206 0.16 UBF5-list.txt 0.04
UBF6 1486 12.05 UBF6-list.txt 0.81
EUF3 5 0.00 EUF3-list.txt 0.00
EUF4 15 0.00 EUF4-list.txt 0.00
EUF5 52 0.02 EUF5-list.txt 0.01
EUF6 203 0.34 EUF6-list.txt 0.07
EU3 4 0.00 EU3-list.txt 0.00
EU4 10 0.00 EU4-list.txt 0.00
EU5 26 0.00 EU5-list.txt 0.00
EU6 76 0.00 EU6-list.txt 0.02
EBF3 5 0.00 EBF3-list.txt 0.00
EBF4 15 0.00 EBF4-list.txt 0.00
EBF5 52 0.05 EBF5-list.txt 0.01
EBF6 203 1.46 EBF6-list.txt 0.16
BF3 4 0.00 BF3-list.txt 0.00
BF4 10 0.00 BF4-list.txt 0.00
BF5 26 0.03 BF5-list.txt 0.01
BF6 76 0.45 BF6-list.txt 0.08
EB3 4 0.00 EB3-list.txt 0.00
EB4 8 0.00 EB4-list.txt 0.00
EB5 16 0.05 EB5-list.txt 0.00
EB6 32 1.16 EB6-list.txt 0.05
LUBF3 10 0.00 LUBF3-list.txt 0.00
LUBF4 142 0.01 LUBF4-list.txt 0.00
LUBF5 1166 2.37 LUBF5-list.txt 0.83
LUBF6 12796 137 LUBF6-list.txt 17.06
LUBF7 183772 255 LUBF7-list.txt 274
LUBF8 3221660 >14h LUBF8-list.txt.bz2 129

Note: DSHARP did not terminate after 14 hours for LUBF8-cnf.txt. The count there was verified by cachet (ca. 4h) and the listing from nbc_minisat_all.

Enumeration details

The description of the special classes is via compulsory minors. The axiomatization uses the complementary class of forbidden minors. CNF files are created by first taking the gaussoid axioms from Enumerating Gaussoids and then for every forbidden minor appending a small set of axioms which forbid this minor. For example a disjunction over all 2-faces of the 3-cube forbids texttt E, or requiring that for every 2-face, its opposite face has to be inside the gaussoid, forbids singletons.

Acknowledgements

To produce the listings, we used Takahisa Toda's and Takehide Soh's AllSAT solvers on the resulting CNF files and condensed its output using the minisat2binary.pl script from Enumerating Gaussoids.

The number of entries in each listing was verified by independently running the SAT counters sharpSAT (in the paper) and DSHARP (in preparation for publishing the data) on the same CNF files.