Speaker: Jessica Striker (North Dakota State University)

Title: Toggling, rowmotion, and homomesy on interval-closed sets

Abstract: Interval-closed sets of a poset are a natural superset of order ideals. We initiate the study of interval-closed sets of finite posets from enumerative and dynamical perspectives. In particular, we use the generalized toggle group to define rowmotion on interval-closed sets as a product of these toggles. Our main theorem is an intricate global characterization of rowmotion on interval-closed sets, which we show is equivalent to the toggling definition. We also study specific posets, proving further results about enumeration and homomesy. This is joint work with Jennifer Elder, Nadia Lafreniere, Erin McNicholas, and Amanda Welch.

Science Learning Center (SLC), 1.204
800 W. Campbell Road, Richardson, Texas 75080-3021

Natural Sciences & Mathematics
Nathan Williams

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