Divisions of space by parallels

Alexanderson, G. L.; Wetzel, John E.

doi:10.1090/S0002-9947-1985-0797066-2

Divisions of space by parallels
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by G. L. Alexanderson and John E. Wetzel

Trans. Amer. Math. Soc. 291 (1985), 363-377

DOI: https://doi.org/10.1090/S0002-9947-1985-0797066-2

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Abstract:

An arrangement of hyperplanes in ${\mathbb {E}^d}$ is a "plaid" provided its hyperplanes form no multiple flats of intersection and lie in parallel families that are in general position. We develop some geometrically natural formulas for the number of $r$-faces that are formed by such an arrangement.

References

G. L. Alexanderson and John E. Wetzel, Arrangements of planes in space, Discrete Math. 34 (1981), no. 3, 219–240. MR 613402, DOI 10.1016/0012-365X(81)90002-9
Gerald L. Alexanderson and John E. Wetzel, Simple partitions of space, Math. Mag. 51 (1978), no. 4, 220–225. MR 506723, DOI 10.2307/2689466
R. C. Buck, Partition of space, Amer. Math. Monthly 50 (1943), 541–544. MR 9119, DOI 10.2307/2303424
Henry W. Gould, Combinatorial identities, Henry W. Gould, Morgantown, W. Va., 1972. A standardized set of tables listing 500 binomial coefficient summations. MR 0354401

Convex polytopes

P. McMullen and G. C. Shephard, Convex polytopes and the upper bound conjecture, London Mathematical Society Lecture Note Series, vol. 3, Cambridge University Press, London-New York, 1971. Prepared in collaboration with J. E. Reeve and A. A. Ball. MR 0301635
John Riordan, Combinatorial identities, Robert E. Krieger Publishing Co., Huntington, N.Y., 1979. Reprint of the 1968 original. MR 554488

Einige Gesetze über die Theilung der Ebene und des Raumes

1

Thomas Zaslavsky, A combinatorial analysis of topological dissections, Advances in Math. 25 (1977), no. 3, 267–285. MR 446994, DOI 10.1016/0001-8708(77)90076-7
Thomas Zaslavsky, Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc. 1 (1975), no. issue 1, 154, vii+102. MR 357135, DOI 10.1090/memo/0154