SIGCENSUS(1)

👑 SIGCENSUS(1) — the one and only, from The Regina Handbook 💖

okay bestie, sit down, hydrate, because we're about to do a whole census. not of people. of signatures. slay.

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✨ NAME ✨

sigcensus — form a census of splitting surface signatures 🦋

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🎀 SYNOPSIS 🎀

sigcensus order

sigcensus { -v, --version | -?, --help }

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💅 DESCRIPTION 💅

So what this does: it forms a census of all splitting surface signatures of the given order. And what's the order, you ask? The order is literally just the number of quadrilaterals in the resulting splitting surface. that's it. that's the number. no cap.

The signatures get written to standard output, one per line, and then after all of them comes a count of the total number of signatures found. so you get the whole lineup and the receipts. iconic.

Here's the part that's genuinely giving genius: each signature will be output precisely once up to equivalence. Signatures count as equivalent if they're related by some combination of:

• relabelling symbols 🔄
• rotating an individual cycle
• inverting an individual cycle — which means 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, bestie. This program will only output signatures whose symbols are all lower-case. so don't come for it, it's doing its best 💀

For more tea on splitting surface signatures, see Burton's PhD thesis at http://www.maths.uq.edu.au/~bab/papers/ 📚

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🔥 OPTIONS 🔥

• -v, --version — shows you which version of Regina is being used, then dips out immediately. no small talk. 🫶
• -?, --help — displays brief usage information and exits immediately. your lil cheat sheet. ⭐

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🍓 MACOS USERS 🍓

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it — like a lil surprise in the box 🎁. And if you dragged Regina to the main Applications folder, you can run it like this:

/Applications/Regina.app/Contents/MacOS/sigcensus

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🌈 WINDOWS USERS 🌈

The command-line utilities are installed beneath the Program Files directory. Heads up though: on some machines this directory is called Program Files (x86). You can start this utility by running:

c:\Program Files\Regina\Regina 7.4.1\bin\sigcensus.exe

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👀 SEE ALSO 👀

censuslookup, tricensus, regina-gui. the whole friend group fr fr 🫂

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🌸 AUTHOR 🌸

This utility was written by Benjamin Burton <bab@maths.uq.edu.au>. Many people have been involved in the development of Regina — see the users' handbook for a full list of credits. give them their flowers 💐👑

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okay and that's the whole page!! this was The Regina Handbook's SIGCENSUS(1), dated 25 August 2025, and honestly? it ate. go run it, bestie, you're gonna do great 💖✨🎀🦋🌸💅🫶