Noncrossing partitions, toggles, and homomesy
1 : Dept. of Mathematics, University of Massachusetts Lowell
MA 01854 -
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2 : Department of Mathematics [MIT]
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Website
Headquarters Office Building 2, Room 236 77 Massachusetts Avenue Cambridge, MA 02139-4307 -
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3 : Department of Mathematics [Minneapolis]
University of Minnesota, Minneapolis, MN, 55455 -
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4 : Department of Mathematics [Storrs]
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Website
University of Connecticut44 Weaver Road, Unit 5233, Storrs, CT 06269-5233, USA -
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5 : Department of Mathematical Sciences [Clemson]
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Website
School of Mathematical and Statistical Sciences | O-110 Martin Hall, Box 340975, Clemson, SC 29634 -
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6 : Euler Circle, Palo Alto, CA
We introduce n(n − 1)/2 natural involutions (“toggles”) on the set S of noncrossing partitions π of size n, along with certain composite operations obtained by composing these involutions. We show that for many operations T of this kind, a surprisingly large family of functions f on S (including the function that sends π to the number of blocks of π) exhibits the homomesy phenomenon: the average of f over the elements of a T -orbit is the same for all T -orbits. Our methods apply more broadly to toggle operations on independent sets of certain graphs.
| Subject : | : | Poster |
| Topics | : | Combinatorics |
| PDF version | : |  PDF version |
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