Waterloo C&O Conference

18Jun07

My department, Combinatorics and Optimization, is hosting a conference this week in honour of its 40th anniversary. So things are about to get a little more nerdy on this blog as I will be mentioning some of the talk details.

For today, at least: a picture! (click for big-ass pdf)

Uncrossing Partitions

It’s my contribution for today’s poster session. Now it’s time to go get free conference coffee, yum!

Update: the first talk of the morning was by Richard Stanley; not a household name perhaps (who is anyway? — Perelman and Wiles?) but the organizers evidently wanted to motivate people to wake up and go to the morning session. His alternating partition survey had a number of interesting results, including the following.

Shuffle a large deck of cards numbered 1 to and look at the first card. Then, for each of the remaining n-1 cards, flip it over and say if it is higher (H) or lower (L) than the previous. The most likely sequences of H’s and L’s are HLHLHLHL… and LHLHLHLH… .

In comparison, for example, the sequence HHHHHH… is very unlikely and can only occur when the cards are sorted into increasing order by the shuffle.

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