Back in my chemistry-PhD days — modelling how molecules fly apart — I kept running into a tidy sort of matrix called a circulant. I spotted a small pattern hiding in them and, around 2011, wrote it up. Then life did its thing: work, moves, the usual entropy. The write-up went in a drawer, and somewhere along the way I lost the original .tex file completely.

This year, with my stack finally empty (see: Writing again), I dug it out, rebuilt it from an ancient PDF, and checked the maths until the computer and I agreed to about twelve decimal places. Then I sent it to a journal. Desk-rejected — no review. I tried a second, more specialised one. Desk-rejected again, this time after a “consultation with a specialist.”

Nobody quite warns you that this kind of rejection isn’t a ruling that you’re wrong. It’s a ruling that you’re not new enough. The result is correct, and apparently rather elegant — but circulants have been thoroughly adored by mathematicians for a century, and “correct and elegant” doesn’t always earn a slice of a journal’s attention. Fair enough.

I could have kept knocking on doors. I didn’t fancy it. (arXiv, the usual home for these things, now wants an institutional sponsor I don’t have — the perks of being an unaffiliated, semi-retired bloke who does crowd control for beer Sprite money.) So I did the unglamorous, oddly liberating thing and published it myself, with a proper DOI, free for anyone to read.

It’s finished. It exists. It has my name on it and a permanent address. That’ll do.

→ Spectral persymmetry of complex circulant and skew-circulant matrices