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Lattice invariant valuations on rational polytopes. (English) Zbl 0387.52007

MSC:
52Bxx Polytopes and polyhedra
52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
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[1] E.Ehrhart, Polynomes arithmetiques et methode des poly?dres en combinatoire. Basel-Stuttgart 1976.
[2] H. Hadwiger, Translationsinvariante, additive und schwachstetige Polyederfunktionale. Arch. Math.3, 387-394 (1952). · Zbl 0048.28801 · doi:10.1007/BF01899378
[3] P. McMullen, Non-linear angle-sum relations for polyhedral cones and polytopes. Math. Proc. Cambridge Phil. Soc.78, 247-261 (1975). · Zbl 0313.52005 · doi:10.1017/S0305004100051665
[4] P. McMullen, Valuations and Euler-type relations on certain classes of convex polytopes Proc. London Math. Soc. (3)35, 113-135 (1977). · Zbl 0353.52001 · doi:10.1112/plms/s3-35.1.113
[5] G.-C. Rota, On the foundations of combinatorial theory, I: Theory of M?bius functions. Z. Wahrscheinlichkeitstheorie2, 340-368 (1964). · Zbl 0121.02406 · doi:10.1007/BF00531932
[6] D. M. Y. Sommerville, The relations connecting the anglesums and volume of a polytope in space of re dimensions. Proc. Roy. Soc. London Ser. A115, 103-119 (1927). · JFM 53.0578.03 · doi:10.1098/rspa.1927.0078
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