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 > Gunawan Emily

Tuesday 5
Combinatorics
Eric Fusy
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
Noncrossing partitions, toggles, & 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 Math, University of Massachusetts Lowell
2 : Dept of Math, Massachusetts Institute of technology [Cambridge]  (MIT)
3 : School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
4 : Dept of Math, University of Connecticut
5 : Dept of Mathematical Sciences, Clemson University
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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