ELECTRONIC CATALOGUE OF REPRESENTATIVES

OF EXTREME SUPERMODULAR SET FUNCTIONS

OVER FIVE VARIABLES


The catalogue is a result of the work described in the research report There are three versions of the catalogue.

The first (older) version of the catalogue is a computer program viewer5.exe (45kB) which can be downloaded using ftp and installed on PC under Windows. It allows one to browse through a list of representatives of types of skeletal imsets which has 1319 items. Each item is then visualised in the form of a diagram. The program needs also the file mfc42.dll (996kB) (do not rename it) and data file *.prn containing vector description of representatives to be visualised. The program allows one to visualise simultaneously two (different) representatives of the same type of skeletal imsets and print such pictures. The following data files are available.

m.prn (94kB) ... standard representatives of types of skeletal imsets
a.prn (94kB) ... incremental transformation of standard representatives
r.prn (94kB) ... reverse (standard) representatives
h.prn (98kB) ... polymatroid representatives
t.prn (99kB) ... Moebius inversion of standard representatives

The second version is a series of online viewers. Each of five viewers uses just one of five ways of representation, namely

ImsetViewM.html ... standard representatives of types of skeletal imsets
ImsetViewA.html ... incremental transformation of standard representatives
ImsetViewR.html ... reverse (standard) representatives
ImsetViewH.html ... polymatroid representatives
ImsetViewT.html ... Moebius inversion of standard representatives
and also allows one to browse through 1319 types of skeletal imsets visualised in the form of diagrams. Moreover, using a special mode, one can fix a certain type and browse through all skeletal imsets belonging to that type. Thus, all 117978 skeletal imsets can be visualised. The viewer uses JAVA and is well accessible with any java enabled browser (such as NETSCAPE version 4.07 or later and Internet Explorer version 4 or later).

The third version of the catalogue is the file fivevar.xls (5522kB) (zipped version fivevar.xls.zip (853kB)) which can be downloaded by ftp and put on PC under Windows. Using EXCEL one can work with vector description of various representatives of types of skeletal imsets. The file also contains several numerical characteristics of every type. The user can arbitrarily reorder the list of representatives on basis of various characteristics, compute further alternative representatives and export them in the form of a file *.prn to be viewed using the above mentioned program Viewer5.exe.

Except the catalogue, computer programs verimpli.exe (50kB) and verstruc.exe (50kB) are available. They can be installed on PC but they also need a special data file m.poi (72kB) and an input text file written in required style (see the research report). The original input file for PORTA fivevar.ieq (4kB) is also available. Morevover, an experimental online version of the program VerifyView.html for verification of facial implication is available (some problems with netscape use can occur).