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Title: PERMUTAEDER Prah, Klara (Author)Kovše, Matjaž (Mentor) More about this mentor... UNI_Prah_Klara_2011.pdf (891,37 KB) Slovenian Undergraduate thesis (m5) FNM - Faculty of Natural Sciences and Mathematics V diplomskem delu bomo podrobneje obravnavali konveksni politop imenovan permutaeder. V prvem poglavju bomo spoznali matematične definicije nekaterih pojmov, ki jih bomo potrebovali v nadaljevanju. V drugem poglavju si bomo pogledali dokaz, da je graf permutaedra hamiltonski graf. V tretjem poglavju bomo dokazali, da razdalje med oglišči v n-dimenzionalnem permutaedru zavzemajo vsa soda števila. V četrtem poglavju si bomo pogledali asociaeder, ki posplošuje permutaeder. permutaeder, zonotop, konveksni politop, hamiltonski graf, minkowskyjeva vsota, Caylejev graf, asociaeder. 2011 [K. Prah] Maribor 51(043.2) 18640904 URN:SI:UM:DK:TWJWL7WT 1481 76 FNM

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## Secondary language

Language: English PERMUTOHEDRON In the thesis we discuss in more detail the convex polytope called permutohedron. In the first chapter we present mathematical definitions of certain concepts which we need later on. In the second chapter we show that the graph of permutohedron is a Hamiltonian graph. In the third chapter we prove that the distances between the vertices in n-dimensional permutohedron take all even numbers. In the fourth chapter we look at another polytope associahedron, which generalizes permutohedron. permutohedron, zonohedron, convex polytopes, Hamiltonian graphs, Minkowski sum, Cayley graph, associahedron.