Balancing pairs and the cross product conjecture

Order - 1995
Graham Brightwell1, Stefan Felsner2, William T. Trotter3
1Department of Mathematics, London School of Economics, London, U.K.
2Fachbereich Mathematik, Institut für Informatik, Freie Universität Berlin, Berlin, Germany
3Department of Mathematics, Arizona State University, Tempe, U.S.A.

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Ahlswede, R. and Daykin, D. E. (1978) An inequality for the weights of two families of sets, their unions and intersections,Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 43, 183?185.

Brightwell, G. (1988) Linear extensions of infinite posets,Discrete Mathematics 70, 113?136.

Brightwell, G. (1989) Semiorders and the 1/3?2/3 conjecture,Order 5, 369?380.

Brightwell, G. (1990) Events correlated with respect to every subposet of a fixed poset,Graphs and Combinatorics 6, 111?131.

Brightwell, G. and Wright, C. D. (1992) The 1/3?2/3 conjecture for 5-thin posets,SIAM J. Discrete Math. 5, 467?474.

Felsner, S. and Trotter, W. T. (1993) Balancing pairs in partially ordered sets, inCombinatorics, Vol. 1, Paul Erdos is Eighty, pp. 145?157.

Fishburn, P. C. (1984) A correlational inequality for linear extensions of a poset,Order 1, 127?137.

Fishburn, P., Gehrlein, W. G., and Trotter, W. T. (1992) Balance theorems for height-2 posets,Order 9, 43?53.

Fredman, M. (1976) How good is the information theoretic bound in sorting?Theoretical Computer Science 1, 355?361.

Friedman, J. (1993) A Note on Poset Geometries,SIAM J. Computing 22, 72?78.

Kahn, J. and Kim, J. Entropy and sorting,JACM, to appear.

Kahn, J. and Linial, N. (1991) Balancing extensions via Brunn-Minkowski,Combinatorica 11, 363?368.

Kahn, J. and Saks, M. (1984) Balancing poset extensions,Order 1, 113?126.

Khachiyan, L. (1989) Optimal algorithms in convex programming decomposition and sorting, in J. Jaravlev (ed.),Computers and Decision Problems, Nauka, Moscow, pp. 161?205 (in Russian).

Kislitsyn, S.S. (1968) Finite partially ordered sets and their associated sets of permutations,Matematicheskiye Zametki 4, 511?518.

Koml�s, J. (1990) A strange pigeon-hole principle,Order 7, 107?113.

Linial, N. (1984) The information theoretic bound is good for merging,SIAM J. Computing 13, 795?801.

Saks, M. (1985) Balancing linear extensions of ordered sets,Order 2, 327?330.

Shepp, L. A. (1980) The FKG inequality and some monotonicity properties of partial orders,SIAM J. Alg. Disc. Meths. 1, 295?299.

Trotter, W. T. (1995) Partially ordered sets, in R. L. Graham, M. Gr�tschel, and L. Lov�sz (eds),Handbook of Combinatorics, to appear.

Trotter, W. T. (1991)Combinatorics and Partially Ordered Sets: Dimension Theory, The Johns Hopkins University Press, Baltimore, MD.