Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Macauley Matthew

Noncrossing partitions, toggles, and homomesy
David Einstein  1  , Miriam Farber  2  , Emily Gunawan  3  , Michael Joseph  4  , Matthew Macauley  5  , James Propp  1  , Simon Rubinstein-Salzedo  6  
1 : Dept. of Mathematics, University of Massachusetts Lowell
MA 01854 -  États-Unis
2 : Department of Mathematics [MIT]  -  Website
Headquarters Office Building 2, Room 236 77 Massachusetts Avenue Cambridge, MA 02139-4307 -  États-Unis
3 : Department of Mathematics [Minneapolis]
University of Minnesota, Minneapolis, MN, 55455 -  États-Unis
4 : Department of Mathematics [Storrs]  -  Website
University of Connecticut44 Weaver Road, Unit 5233, Storrs, CT 06269-5233, USA -  États-Unis
5 : Department of Mathematical Sciences [Clemson]  -  Website
School of Mathematical and Statistical Sciences | O-110 Martin Hall, Box 340975, Clemson, SC 29634 -  États-Unis
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. 

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