2. Articole

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    THE EULER TOUR OFN-DIMENSIONAL MANIFOLDWITH POSITIVE GENUS
    (Institutul de Matematică şi Informatică al AŞM, 2008) Cataranciuc, Sergiu; Bujac-Leisz, Mariana; Soltan, Petru
    In the paper [1] it is proved that abstract cubicn-dimensional torus[2] possesses a directed Euler tour of the same dimension. The result prompts toa new (virtual) device for transmission and reception of information. In the presentpaper it is shown that every abstract cubicn-dimensional manifold without borders, ofpositive genus possesses an-dimensional directed Euler tour. This result has practicalapplication.
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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.