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Combinatorial dimension of fractional Cartesian products. (English) Zbl 0788.90048

Summary: The combinatorial dimension of a fractional Cartesian product is the optimal value of an associated linear programming problem.

MSC:

90C05 Linear programming
05C65 Hypergraphs
43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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References:

[1] Ron C. Blei, Fractional Cartesian products of sets, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 2, v, 79 – 105 (English, with French summary). · Zbl 0381.43003
[2] Ron Blei, Combinatorial dimension and certain norms in harmonic analysis, Amer. J. Math. 106 (1984), no. 4, 847 – 887. · Zbl 0579.43010 · doi:10.2307/2374326
[3] Ron C. Blei, Fractional dimensions and bounded fractional forms, Mem. Amer. Math. Soc. 57 (1985), no. 331, iv+69. · Zbl 0623.26015 · doi:10.1090/memo/0331
[4] Ron C. Blei, Stochastic integrators indexed by a multi-dimensional parameter, Probab. Theory Related Fields 95 (1993), no. 2, 141 – 153. · Zbl 0792.60044 · doi:10.1007/BF01192267
[5] R. C. Blei and T. W. Körner, Combinatorial dimension and random sets, Israel J. Math. 47 (1984), no. 1, 65 – 74. · Zbl 0533.43002 · doi:10.1007/BF02760562
[6] Ron C. Blei and J.-P. Kahane, A computation of the Littlewood exponent of stochastic processes, Math. Proc. Cambridge Philos. Soc. 103 (1988), no. 2, 367 – 370. · Zbl 0654.60006 · doi:10.1017/S030500410006494X
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