# Whirling injections, surjections, and other functions between finite sets

@article{Joseph2017WhirlingIS, title={Whirling injections, surjections, and other functions between finite sets}, author={Michael Joseph and James Gary Propp and Tom Roby}, journal={arXiv: Combinatorics}, year={2017} }

This paper analyzes a certain action called "whirling" that can be defined on any family of functions between two finite sets equipped with a linear (or cyclic) ordering. As a map on injections and surjections, we prove that within any whirling-orbit, any two elements of the codomain appear as outputs of functions the same number of times. This result, can be stated in terms of the homomesy phenomenon, which occurs when a statistic has the same average across every orbit. We further explore…

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