2. Articole

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    ON THE DIVISION OF ABSTRACT MANIFOLDS IN CUBES
    (Institutul de Matematică şi Informatică al AŞM, 2006) Bujac, Mariana; Cataranciuc, Sergiu; Soltan, Petru
    We prove that in the class of abstract multidimensional manifolds withoutborders only torusVn1of dimensionn≥1 can be divided in abstract cubes with theproperty: every faceImfromVn1is shared by 2n−mcubes,m= 0,1, . . . , n−1. Theabstract torusVn1is realized inEd, n+1≤d≤2n+1, so it results that in the class ofalln-dimensional combinatorial manifolds [1]onlytorus respects this propriety. Torusis autodual because of this propriety.