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Euler's relation,möbius functions and matroid identities |
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| Authors: | Raul Cordovil Michel Las Vergnas Arnaldo Mandel |
| Affiliation: | (1) C. F. M. C. Inst. Nac. Inv. Cient, Av. Prof. Gama Pinto 2, Lisboa 4, Portugal;(2) Centre National de la Recherche, Scientifique, Université Pierre et Marie Curie, U. E. R. 48, 4 place Jussieu, 75005 Paris, France;(3) Instituto de Matématica e Estatistica, U. S. P. Sao Paul, Brazil |
| Abstract: | We give a short combinatorial proof of the Euler relation for convex polytopes in the context of oriented matroids. Using counting arguments we derive from the Euler relation several identities holding in the lattice of flats of an oriented matroid. These identities are proven for any matroid by Möbius inversion. |
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