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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Cordovil, R., Las Vergnas, M. & Mandel, A. Euler's relation, möbius functions and matroid identities. Geom Dedicata 12, 147–162 (1982). https://doi.org/10.1007/BF00147634
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DOI: https://doi.org/10.1007/BF00147634