The Dittert conjecture, or Dittert-Hajek conjecture, is a hypothesis in combinatorics about the maximum achieved by a particular function of square matrices with real, nonnegative entries whose row and column sums total the matrix order. It is due to Eric Dittert and, independently, Bruce Hajek, and asserts the function is uniquely maximized when every entry equals one divided by the matrix order. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementThe function phi(A), equal to the product of the row sums of A plus the product of the column sums of A minus the permanent of A, is uniquely maximized when every entry of the n by n nonnegative matrix A equals 1 divided by n, that is, when A is 1/n times the all ones matrix Jn. 1 Progress Toward ResolutionPartial progress toward the conjecture was made by Gi-Sang Cheon and Ian M. Wanless in their 2012 paper Some Results towards the Dittert Conjecture on Permanents; the conjecture remains unproven in general. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Dittert Conjecture (Wikipedia)
Sources
1. Dittert Conjecture (Wikipedia)
Wikimedia FoundationLead section
The conjecture is due to Eric Dittert and (independently) Bruce Hajek.
Statement section
is (uniquely) maximized when A = (1/n)Jn, where Jn is the square matrix of order n with all entries equal to 1
References section
Cheon, Gi-Sang; Wanless, Ian M. (15 February 2012). "Some results towards the Dittert conjecture on permanents"
In Branch: Combinatorics, Lead sentence
Hajek conjecture, is a mathematical hypothesis in combinatorics concerning the maximum achieved by a particular function ϕ of matr
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.