LIP6 1998/050

• Reports
  Propriétés combinatoires des matrices sur les (pré)-semi-anneaux
• M. Minoux
• 45 pages - 12/31/1998- document en - http://www.lip6.fr/lip6/reports/1998/lip6.1998.050.ps.gz - 103 Ko
• Contact : Michel.Minoux (at) nulllip6.fr
• Ancien Thème : ANP
Many classical properties of real matrices actually derive from purely combinatorial properties which remain valid in algebraic structures much more general than the field of real numbers, namely semi-rings and pre-semi-rings. We present here generalizations to semi-rings of :
- the CAYLEY-HAMILTON Theorem ;
- the so-called "Matrix Tree Theorem" due to BORCHARDT and TUTTE, and its extended version, the "All Minors Matrix Tree Theorem".
- the MACMAHON "Master Theorem".
• Keywords : semi-rings, pre-semi-rings, bideterminant
• Publisher : Emmanuelle.Encrenaz (at) nulllip6.fr