A refined Razumov-Stroganov conjecture

P. Di Francesco

doi:10.1088/1742-5468/2004/08/p08009

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arXiv · cond-mat/0407477

A refined Razumov-Stroganov conjecture

P. Di Francesco

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Abstract

We extend the Razumov-Stroganov conjecture relating the groundstate of the O(1) spin chain to alternating sign matrices, by relating the groundstate of the monodromy matrix of the O(1) model to the so-called refined alternating sign matrices, i.e. with prescribed configuration of their first row, as well as to refined fully-packed loop configurations on a square grid, keeping track both of the loop connectivity and of the configuration of their top row. We also conjecture a direct relation between this groundstate and refined totally symmetric self-complementary plane partitions, namely, in their formulation as sets of non-intersecting lattice paths, with prescribed last steps of all paths.

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P. Di Francesco. 2004-09-08. A refined Razumov-Stroganov conjecture. https://doi.org/10.1088/1742-5468%2F2004%2F08%2Fp08009

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