The Toggle Group, Homomesy, and the Razumov-Stroganov Correspondence

  • Jessica Striker
Keywords: Posets, Alternating sign matrices, Loop models


The Razumov-Stroganov correspondence, an important link between statistical physics and combinatorics proved in 2011 by L. Cantini and A. Sportiello, relates the ground state eigenvector of the $O(1)$ dense loop model on a semi-infinite cylinder to a refined enumeration of fully-packed loops, which are in bijection with alternating sign matrices. This paper reformulates a key component of this proof in terms of posets, the toggle group, and homomesy, and proves two new homomesy results on general posets which we hope will have broader implications.

Author Biography

Jessica Striker, North Dakota State University
Mathematics Department, Assistant Professor
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