Van der Waerden’s permanent conjecture

Let A be any doubly stochastic n×n matrix (i.e. nonnegative real entries, each row sums to 1, each column too, hence square).

Let A be the one where all entries are equal (i.e. they are 1n). Its permanentMathworldPlanetmath works out to


and Van der Waerden conjectured in 1926 that this is the smallest value for the permanent of any doubly stochastic A, and is attained only for A=A:

perA>n!(1n)n(for AA).

It was finally proven independently by Egorychev and by Falikman, in 1979/80.


  • 1
  • Hal86 Marshall J. Hall, Jr., Combinatorial Theory (2nd ed.),
    Wiley 1986, repr. 1998, ISBN  0 471 09138 3 and 0 471 31518 4
    has a proof of the permanent conjecture.
Title Van der Waerden’s permanent conjecture
Canonical name VanDerWaerdensPermanentConjecture
Date of creation 2013-03-22 15:10:51
Last modified on 2013-03-22 15:10:51
Owner marijke (8873)
Last modified by marijke (8873)
Numerical id 5
Author marijke (8873)
Entry type Theorem
Classification msc 15A15
Classification msc 15A51
Synonym permanent conjecture