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. 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.
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| - Conjectura de Dittert (ca)
- Dittert conjecture (en)
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| - En combinatòria, la conjectura de Dittert, o conjectura de Dittert-Hajek, és una hipòtesi matemàtica relativa al màxim assolit per una determinada funció de matrius amb entrades reals i no negatives que compleixin una condició sumatòria. La conjectura es deu a Eric Dittert i (independentment) a Bruce Hajek. Sigui una matriu quadrada d'ordre amb entrades no negatives i amb . Definim com , on la suma s'estén sobre tots els elements del grup simètric. (ca)
- 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. 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. (en)
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| - En combinatòria, la conjectura de Dittert, o conjectura de Dittert-Hajek, és una hipòtesi matemàtica relativa al màxim assolit per una determinada funció de matrius amb entrades reals i no negatives que compleixin una condició sumatòria. La conjectura es deu a Eric Dittert i (independentment) a Bruce Hajek. Sigui una matriu quadrada d'ordre amb entrades no negatives i amb . Definim com , on la suma s'estén sobre tots els elements del grup simètric. La conjectura de Dittert afirma que la funció definida per es maximitza (de manera única) quan , on es defineix com la matriu quadrada d'ordre amb totes les entrades iguals 1. (ca)
- 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. 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. (en)
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