Dittert conjecture

The Dittert conjecture, or Dittert–Hajek conjecture, is a mathematical hypothesis (in combinatorics) concerning the maximum achieved by a particular function of matrices with real, nonnegative entries satisfying a summation condition. The conjecture is due to Eric Dittert and (independently) Bruce Hajek.[1][2][3][4]

Let be a square matrix of order with nonnegative entries and with . Its permanent is defined as , where the sum extends over all elements of the symmetric group.

The Dittert conjecture asserts that the function defined by is (uniquely) maximized when , where is defined to be the square matrix of order with all entries equal to 1.[1][2]

References

  1. Hogben, Leslie, ed. (2014). Handbook of Linear Algebra (2nd ed.). CRC Press. pp. 43–8.
  2. Cheon, Gi-Sang; Wanless, Ian M. (15 February 2012). "Some results towards the Dittert conjecture on permanents". Linear Algebra and its Applications. 436 (4): 791–801. doi:10.1016/j.laa.2010.08.041.
  3. Eric R. Dittert at the Mathematics Genealogy Project
  4. Bruce Edward Hajek at the Mathematics Genealogy Project


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.