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stoutfellowLast week, I gave my History of Math students a list of possible topics for their first essays. I asked them each to select three topics that they would be interested in doing; I would then select one of their three. I finally got everyone's choices last night, and today tried to reconcile them. (I don't want two students doing the same topic.)
It was impossible. I do not use the word lightly; there are theorems in combinatorics which address the question of "matchings", as they are called, and one in particular that gives a necessary condition for their possibility. The lists of preferences I was given did not meet that condition.
Fortunately, one student had given me a preference-order for the entire list, rather than just three. Poor guy wound up with his seventh choice (out of twenty-nine), but any other assignment would have been purely arbitrary.
It was impossible. I do not use the word lightly; there are theorems in combinatorics which address the question of "matchings", as they are called, and one in particular that gives a necessary condition for their possibility. The lists of preferences I was given did not meet that condition.
Fortunately, one student had given me a preference-order for the entire list, rather than just three. Poor guy wound up with his seventh choice (out of twenty-nine), but any other assignment would have been purely arbitrary.
