Geodesic
The toggle group, homomesy, and the Razumov-Stroganov correspondence
Jessica Striker1
1North Dakota State University
The electronic journal of combinatorics, Tome 22 (2015) no. 2
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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.
DOI : 10.37236/5158
Classification : 05A15, 06A07, 82B20, 82B23
Mots-clés : posets, alternating sign matrices, loop models

Jessica Striker  1

1 North Dakota State University 
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Jessica Striker. The toggle group, homomesy, and the Razumov-Stroganov correspondence. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/5158

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