We prove the so-called Razumov-Stroganov sum-rule conjecture, by relating the partition functions of inhomogeneous O(1) loop model on a semi-infinite cylinder on one hand, and of the inhomogeneous six-vertex model with domain-wall boundary conditions at a special value of the anisotropy parameter $q=e^{2ipi/3}$ on the other hand. The latter is known as the Izergin-Korepin determinant. Using mainly the Yang-Baxter equation, we show that both functions satisfy the same defining properties and recursion relations.

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