Proof of the alternating sign matrix conjecture

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Abstract

The number of n × n matrices whose entries are either -1, 0, or 1, whose row- and column- sums are all 1, and such that in every row and every column the non-zero entries alternate in sign, is proved tobe [1!4!... (3n - 2)!]/[n!(n + 1)!... (2n - 1)!], as conjectured by Mills, Bobbins, and Rumsey.

Original languageEnglish (US)
Article numberR13
Pages (from-to)1-84
Number of pages84
JournalElectronic Journal of Combinatorics
Volume3
Issue number2 R
StatePublished - 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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