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Contributions to the geometry of Hamming spaces. (English) Zbl 0368.05001

MSC:
05A05 Permutations, words, matrices
51N99 Analytic and descriptive geometry
52A40 Inequalities and extremum problems involving convexity in convex geometry
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[1] Ahlswede, R.; Körner, J., Source coding with side information and a converse for degraded broadcast channels, IEEE trans. information theory, 21, 592-637, (1975) · Zbl 0315.94016
[2] Ahlswede, R.; Gáces, P.; Körner, J., Bounds on conditional probabilities and applications in multiuser communication, Z. wahrscheinlichkeitstheorie und verw. geb., 34, 157-177, (1978)
[3] Bernstein, A.J., Maximally connected arrays on the n-cube, SIAM J. appl. math., 15, 1485-1489, (1967) · Zbl 0157.26004
[4] Bieberbach, L., Über eine extremaleigenschaft des kreises, Jber. dtsch. math. ver., 24, 247-250, (1915) · JFM 45.0623.01
[5] Brunn, H., Über ovale und eiflächen, Inaugural diss., (1887), München · JFM 19.0615.01
[6] Clements, G.F.; Lindström, B., A generalization of a combinatorial theorem of Macaulay, J. combinatorial theory, 7, 230-238, (1969) · Zbl 0186.01704
[7] Clements, G.F., Sets of lattice points which contain a maximal number of edges, Proc. am. math. soc., 27, 13-15, (1971) · Zbl 0216.02001
[8] Daykin, D.E., A simple proof of the Kruskal-katona theorem, J. combinatorial theory, 17, 252-253, (1974) · Zbl 0287.05004
[9] J. Eckhoff and G. Wegner. Über einen Satz von Kruskal, Periodica, to appear. · Zbl 0284.05010
[10] Erdös, P.; Kleitman, D.J., Extremal problems among subsets of a set, Proc. second chapel Hill conf. on combinatorial mathematics and its applications, 146-170, (1970), Chapel Hill, N.C.
[11] Erdös, P.; Chao, Ko; Rado, R., Intersection theorems for systems of finite sets, Quart. J. math. Oxford ser., 12, 48, (1961) · Zbl 0100.01902
[12] C. Greene and D.J. Kleitman, Proof Techniques in the Theory of Finite Sets, MIT Lecture Notes. · Zbl 0409.05012
[13] C. Greene, G.O.H. Katona and D.J. Kleitman, Extensions of the Erdös-Ko-Rado Theorem. Submitted to the Proceedings of the Second Prague Conference on Graph Theory. · Zbl 0331.05001
[14] Hamming, R.W., Error detecting and error correcting codes, Bell system tech. J., 29, 147-160, (1950) · Zbl 1402.94084
[15] Harper, L.H., Optimal assignments of numbers to vertices, J. soc. industr. appl. math., 12, 131-135, (1964) · Zbl 0222.94004
[16] G.O.H. Katona, The Hamming sphere has minimal boundary, To appear in Studio Scj. Math. Hung.
[17] Katona, G.O.H., Intersection theorems for systems of finite sets, Acta math. acad. sci. hungar., 15, 329-337, (1964) · Zbl 0134.25101
[18] Katona, G.O.H., External problems for hypergraphs, Proceedings of the advanced study institute of combinatorics held at nijenrode castle breukelen, (July 8-20, 1974), The Netherlands
[19] Katona, G.O.H., A theorem of finite sets, theory of graphs, (), 187-207 · Zbl 0878.05079
[20] Kleitman, D., On a combinatorial conjecture of Erdös, J. combinatorial theory, 1, 209-214, (1966) · Zbl 0148.01105
[21] Kleitman, D.J., On a conjecture of milner on K-graphs with non-disjoint edges, J. combinatorial theory, 5, 153-156, (1968) · Zbl 0167.22204
[22] Kleitman, D.; Edelberg, M.; Lubell, D., Maximal sized antichains in partial orders, Discrete math., 1, 47-53, (1971) · Zbl 0217.02701
[23] Kruskal, J.B., The number of simplicies in a complex, (), 251-278
[24] Lindsey, J.H., Assignment of numbers to vertices, Am. math. monthly, 71, 508-516, (1964) · Zbl 0279.05019
[25] Macaulay, F.S., Some properties of enumeration in the theory of modular systems, Proc. London math. soc., 26, 531-555, (1927) · JFM 53.0104.01
[26] Margulis, G.A., Probabilistic properties of graphs with large connectivity, Problemy peredac̆i informacii, 10, 101-108, (1974) · Zbl 0322.05147
[27] Minkowski, H., Gesammelte abhandlungen, 2, (1911), Teubner Leipzig
[28] Schmidt, E., Der brunn-minkowskische satz und sein spiegeltheorem sowie die isoperimetrische eigenschaft der kugel in der euklidischen und hyperbolischen geometrie, Math. ann., 120, 307-422, (1948) · Zbl 0036.23801
[29] Schmidt, E.; Schmidt, E., Die brunn-minkowskische ungleichung und ihr spiegelbild sowie die isoperimetrische eigenschaft der kugel in der euklidischen und nicht-euklidischen geometrie II, Math. nachr., Math. nachr., 2, 171-244, (1949) · Zbl 0041.51001
[30] Schwartz, H.A., Beweis des satzes, daβ die kugel eine kleinere oberfläche besitzt als jeder andere Körper gleichen volumens, Nachr akad. wiss. Göttingen math.-phys. kl., 1-13, (1884) · JFM 16.0232.04
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