Around the Razumov-Stroganov conjecture: Proof of a multi-parameter sum rule

P. Di Francesco, P. Zinn-Justin

Research output: Contribution to journalArticlepeer-review


We prove that the sum of entries of the suitably normalized groundstate vector of the O(1) loop model with periodic boundary conditions on a periodic strip of size 2n is equal to the total number of n × n alternating sign matrices. This is done by identifying the state sum of a multi-parameter inhomogeneous version of the O(1) model with the partition function of the inhomogeneous six-vertex model on a n × n square grid with domain wall boundary conditions.

Original languageEnglish (US)
Article numberR6
Pages (from-to)1-27
Number of pages27
JournalElectronic Journal of Combinatorics
Issue number1 R
StatePublished - Jan 11 2005
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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