Monday Discussion on Combinatorial Issues

The disussion was moderated by Michelle Wachs. She started off the discussion by asking:

Q. What combinatorial questions arise in biology that might be of interest to biologists? Or, what problems motivated by biology would be of interest to mathematicians, to give us some interesting problems?

Q. Given a set $S$ of $k$ edges, and a subset $J$ of $S$, how many leaf labeled binary trees have some subset $J$ of $S$ but not the edges in $S-J$? Do this for all $J$.

Q. What are good codings for trees?

Q. Is there an efficient representation for coding trees? (Billera)

Q. Is there a nice neat notation for trees that is continuous when doing a random walk on trees? In other words, do small changes in notation correspond to close trees? (Diaconis)

Q. Are there questions that combinatorialists might have for biologists? Combinatorial structures that biologists might be interesting? (Wachs)

Q. If we took trees and instead of putting real numbers of them, putting discrete values, like 0-1, would that be of interest in biologists? (Diaconis)

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