Name

sigcensus — Form a census of splitting surface signatures

Synopsis

sigcensus {order}

Description

Forms a census of all splitting surface signatures of the given order. The order is the number of quadrilaterals in the resulting splitting surface.

The signatures will be written to standard output, one per line, followed by a count of the total number of signatures found.

Each signature will be output precisely once up to equivalence. Signatures are considered equivalent if they are related by some combination of:

  • relabelling symbols;

  • rotating an individual cycle;

  • inverting an individual cycle (i.e., reversing the cycle and changing the case of each symbol in the cycle);

  • reversing all cycles without changing the case of any symbols.

Upper-case symbols in signatures are not yet supported; this program will only output signatures whose symbols are all lower-case.

For more information on splitting surface signatures, see Burton's PhD thesis at www.maths.uq.edu.au.

MacOS Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged Regina to the main Applications folder, you can run it as /Applications/Regina.app/Contents/MacOS/sigcensus.

Windows Users

The command-line utilities are installed beneath the Program Files directory; on some machines this directory is called Program Files (x86). You can start this utility by running c:\Program Files\Regina\Regina 5.1\bin\sigcensus.exe.

Author

This utility was written by Benjamin Burton . Many people have been involved in the development of Regina; see the acknowledgements page for a full list of credits.