2. Articole

Browse

Now showing 1 - 2 of 2

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.
THE MULTIDIMENSIONAL DIRECTED EULER TOUROF CUBIC MANIFOLD
(Institutul de Matematică şi Informatică al AŞM, 2006) Bujac, Mariana
n the paper [3] we tried to generalize the problem of existence of a di-rected (n−1)-dimensional Euler tour for the abstract directedn-dimensional manifold,which is acomplex of multi-ary relations[5], namely by means of abstract simplexes.In the paper [3] we show the existence of such kind of tour onlyfor manifolds of odddimension because we have not enough conditions to do more. In the present paperwe will show conditions of existence for a directed Euler tour of abstract manifoldswith even dimensions. In this purpose, we will introduce some new definitions whichpermit us to define manifolds by so-calledabstract cubes.