How many Euler circuits are there in the complete directed graph on N vertices? More interesting to me, how many equivalence classes under reversal and relabeling?
| N | circuits: n(n-2) (n-2)!n | classes |
| 3 | 3 | 1 |
| 4 | 256 | 6 |
| 5 | 972000 | 4089 |
| 6 | 247669456896 | ≥171994409 |
As I write this I am waiting for my program to finish counting the classes for six vertices, Continue reading
Most of the bot comments here are on a few posts, for which I have now created a category spambait.
I bought a cat-cave, and Bramble clearly approves, though he still prefers to get under my blankets. If he had his way I’d never get out of bed.
Watching The Long Kiss Goodnight and enjoying it as much as I did in 1996.
I find that I have regularly misquoted a favorite bit of dialogue. My memory for wording is usually better than that. Perhaps I inherited a mild case of Mom’s lifelong malapropism; but that would not explain another anomaly: I also misremembered that Patrick Malahide made an atrocious attempt at a Dixie accent, rather than using his own voice. Perhaps that was another role.
I have often had dreams of futility, which I take to be a sign of depression. For example: there are many scraps of paper on the floor, and I have to find a specific one, but I cannot read.
This morning I had a mild one. I had breakfast at an outdoor restaurant, chatted with the waiter, returned to where I parked my car; it was not there. I later found it a block away, but blocked in by a parked truck. I used my car key to unlock something that released a rope so that the truck (now a trailer) rolled down the street, bumping into another trailer which bumped a third before they all came to rest. But now my car had vanished. I thought, this is too absurd, I’m dreaming. I sat on a bench and said, when I open my eyes that brick building yonder will be something else. It did change but, before I could take in the new scene, something pulled my hair from behind; when I turned to see who or what, I woke up.
Being aware of dreaming, however briefly, is new to me, or quite rare.
Somehow I never had anything by David Bowie in my collection (other than a German version of “Heroes” on some sampler album, and “Under Pressure” on the Grosse Pointe Blank soundtrack) until recently when I picked up Best of Bowie (2002), which makes me wonder what the fuss is about. Perhaps he is celebrated for something other than music?
Okay, “Modern Love” is catchy.
A key scene in the above-titled flick cannot work unless the two leads have very similar breasts; and now I’m curious about the casting process.