DOAJ Open Access 2020

Noncrossing partitions, toggles, and homomesy

David Einstein Miriam Farber Emily Gunawan Michael Joseph Matthew Macauley +2 lainnya

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Abstrak

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.

Topik & Kata Kunci

Mathematics

Penulis (7)

David Einstein

Miriam Farber

Emily Gunawan

Michael Joseph

Matthew Macauley

James Propp

Simon Rubinstein-Salzedo

Format Sitasi

APA MLA BibTeX

Einstein, D., Farber, M., Gunawan, E., Joseph, M., Macauley, M., Propp, J. et al. (2020). Noncrossing partitions, toggles, and homomesy. https://doi.org/10.46298/dmtcs.6378

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6378

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6378
Akses: Open Access ✓