Boolean layer cakes. Proceedings ORDAL '96

Theoretical Computer Science

Volumn 217, Issue 2, 1999, Pages 255-278

  Schmid, J ^a  

^a UNIVERSITY OF BERN   (Switzerland)

Author keywords

Automorphism; Boolean lattice; Maximal sublattice; Order dimension; Suborder

Indexed keywords

EID: 0141549803     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(98)00274-6     Document Type: Article

References (50)

1. M.E. Adams, Ph. Dwinger, J. Schmid, Maximal sublattices of finite distributive lattices, Algebra Universalis, to appear.
2. M.E. Adams, R. Freese, J.B. Nation, J. Schmid, Maximal sublattices and Frattini sublattices of bounded lattices, preprint, 1995.
3. M. Aigner, Lexicographic matching in Boolean algebras, J. Combin. Theory Ser. B 14 (1973) 187-194.
4. G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ., vol. 25, Providence, R.I., 1967.
5. G.R. Brightwell, H.A. Kierstead, A.V. Kostochka, W.T. Trotter, The dimension of suborders of Boolean lattices, Order 11 (1994) 127-134.
6. G.R. Brightwell, H.J. Prömel and A. Steger, The average number of linear extensions of a partial order, J. Combin. Theory Ser. A 73 (1996) 193-206.
7. G. Burosh and J. Laborde, Einbettungen von Graphen in den n-Würfel, in: K. Wagner and H. Bodendiek (Eds.), Graphentheorie III, BI Wissenschaftsverlag, 1992, pp. 73-94.
8. B. Crocker, Cookbook, 21th printing, Golden Press, New York, 1974, pp. 92 and 125.
9. I.J. Dejter, Hamilton cycles and quotients of bipartite graphs, in: Y. Alavi et al. (Eds.), Proc. Vth Internat. Conf. Theory Appl. Graphs, Wiley, New York, 1985, pp. 189-199.
10. I.J. Dejter, W. Cedeño, V. Jauregui, A note on Frucht diagrams, Boolean graphs and Hamilton cycles, Discrete Math. 114 (1993) 131-135.
11. I.J. Dejter, J. Córdova, J. Quintana, Two Hamilton cycles in bipartite reflective Kneser graphs, Discrete Math. 72 (1988) 63-70.
12. D.Z. Djokovič, Distance preserving subgraphs of hypercubes, J. Combin. Theory Ser. B 14 (1973) 263-267.
13. D. Duffus, P. Hanlon, R. Roth, Matchings and Hamiltonian cycles in some families of symmetric graphs, Emory University Technical Report, 1986.
14. D. Duffus, H.A. Kierstead, H.S. Snevily, An explicit 1-factorization in the middle of the Boolean lattice, J. Combin. Theory Series Ser. A 65 (1994) 334-342.
15. D. Duffus, V. Rödl, B. Sands, R. Woodrow, Enumeration of order-preserving maps, Order 9 (1992) 15-29.
16. D. Duffus, B. Sands, P. Winkler, Maximal chains and antichains in Boolean lattices, SIAM J. Discrete Math. 3 (1990) 197-205.
17. D. Duffus, B. Sands, R. Woodrow, Lexicographic matchings cannot form Hamiltonian cycles, Order 5 (1988) 149-161.
18. B. Dushnik, Concerning a certain set of arrangements, Proc. Amer. Math. Soc. 1 (1950) 788-796.
19. B. Dushnik, E.W. Miller, Partially ordered sets, Amer. J. Math. 63 (1941) 600-610.
20. J.D. Farley, The number of order preserving maps between fences and crowns, Order 12 (1995) 5-44.
21. Z. Füredi, The order dimension of two levels of the Boolean lattice, Order 11 (1994) 15-28.
22. Z. Füredi, P. Hajnal, V. Rödl, W.T. Trotter, Interval orders and shift graphs, in: A. Hajnal, V. Sos (Eds.), Sets, Graphs and Numbers, Proc. Colloq. Math. Soc. Janos Bolyai, vol. 60, Budapest, Hungary, 1991, pp. 297-313.
23. Z. Füredi, J. Kahn, On the dimensions of ordered sets of bounded degree, Order 3 (1986) 17-20.
24. Z. Füredi, K. Reuter, The jump number of suborders of the power set order, Order 6 (1989) 101-103.
25. G. Gierz, Level sets in finite distributive lattices of breadth 3, Discrete Math. 132 (1994) 51-63.
26. G. Gierz, F. Hergert, The bandwidth problem for distributive lattices of breadth 3, Discrete Math. 88 (1991) 157-177.
27. F. Harary, J.P. Hayes, H.-J. Wu, A survey of the theory of hypercube graphs, Comput. Math. Appl. 15 (1988) 277-289.
28. J. Hashimoto, Ideal theory for lattices, Math. Japan. 2 (1952) 149-186.
29. G. Havas, M. Ward, Lattices with sublattices of a given order, J. Combin. Theory 7 (1969) 281-282.
30. I. Havel, Semipaths in directed cubes, in: M. Fiedler (Ed.), Graphs and other Combinatorial Topics, Teubner, Leipzig, 1983, pp. 101-108.
31. I. Havel, J. Movárek, B-valuations of graphs, Czech. Math. J. 22 (1972) 338-351.
32. G.H. Hurlbert, A.V. Kostochka, L.A. Talysheva, The dimension of interior levels of the Boolean lattice, Order 11 (1994) 29-40.
33. H.A. Kierstead, On the order dimension of 1-sets versus k-sets, J. Combin. Theory Ser. A 73 (1996) 219-228.
34. H.A. Kierstead, W.T. Trotter, Explicit matchings in the middle levels of the Boolean lattice, Order 5 (1988) 163-171.
35. D.J. Kleitman, B.L. Rothschild, Asymptotic enumeration of partial orders on a finite set, Trans. Amer. Math. Soc. 205 (1975) 205-220.
36. A.D. Korshunov, On the number of monotone Boolean functions, Probl. Kibern. 38 (1981) 5-108 (in Russian).
37. D.W. Krumme, K.N. Venkataraman, G. Cybenko, Hypercube embedding is NP-complete, in: M.T. Heath (Ed.), Proc. 1st Conf. on Hypercube Multiprocessors, SIAM, Philadelphia, 1986, pp. 148-157.
38. L. Lippert, Automorphismen Boole'scher Schichtenkuchen, Masters Thesis, University of Bern, in preparation.
39. W.-P. Liu, I. Rival, N. Zaguja, Automorphisms, isotone self-maps and cycle-free orders, Discrete Math. 144 (1995) 59-66.
40. W.-P. Liu, H. Wan, Automorphisms and isotone self-maps of ordered sets with top and bottom, Order 10 (1993) 105-110.
41. Z. Lonc, Partitions of large Boolean lattices, Discrete Math. 131 (1994) 173-181.
42. J. Mitas, K. Reuter, Cover-preserving embeddings of bipartite orders into Boolean lattices, Theoret. Comput. Sci., to appear.
43. J. Mitas, K. Reuter, Subgraphs of hypercubes and subdiagrams of Boolean lattices, preprint, December 1995.
44. M. Nüssli, Maximale Unterverbände Boole'scher Schichtenkuchen, Master's Thesis, University of Bern, 1996 (unpublished).
45. I. Rival, A. Rutkowski, Does almost every isotone self-map have a fixed point?, in: Extremal problems for Finite Sets, Bolyai Soc. Math. Studies, vol. 3, Visegrad, Hungary, 1991, pp. 413-422.
46. J. Spencer, Minimal scrambling sets of simple orders, Acta Math. Acad. Sci. Hung. 22 (1971) 349-353.
47. W.T. Trotter, Some combinatorial problems for permutations, Congressus Numerantium 19 (1978) 179-191.
48. W.T. Trotter, Combinatorics and Partially Ordered Sets: Dimension Theory, John Hopkins Univ. Press, Baltimore, 1992.
49. M. Wild, Cover-preserving order embeddings into Boolean lattices, Order 9 (1992) 209-232.
50. N. Zaguia, Isotone maps: Enumeration and structure, in: N.W. Sauer, R.E. Woodrow, B. Sands (Eds.), Finite and Infinite Combinatorics in Sets and Logic, NATO ASI Series, Series C: Math. and Phys. Sci., vol. 411, Kluwer Acad. Publ., Dordrecht, 1993, pp. 421-430.