Lattices of SK-Partitions
Abstract:
Lattice theory and combinatorial set theory are applied in the study of SK-partitions. The rank function of a lattice SK-partitions is investigated and bounds are obtained for the sizes of chains, antichains and other subsets. Regular, geometric lattices of SK-partitions are also considered. Lattice theory has now many upcoming modern applications.
How to cite this article
Shanaz Ansari Wahid, Norris Sookoo and Ashok Sahai, 2007. Lattices of SK-Partitions. Journal of Applied Sciences, 7: 2366-2370.
REFERENCES
Calteneo, G. and D. Ciucci, 2004. On the lattice structure of preclusive rough sets. Proceedings of the International Conference on Fuzzy Systems, July 25-29, 2004, IEEE Computer Society Washington, DC., USA., pp: 121-126.
Canfield, E.R., 1998. The size of the largest antichain in the partition lattice. J. Combinatorial Theory, Ser. A, 83: 188-201.
Direct Link
Delsarte, P., 1976. Association schemes and t-designs in regular semilattices. J. Combinatorial. Theory, Ser. A, 20: 230-243.
Delsarte, P., 1977. Hahn polynomials, discrete harmonics and t-designs. Siam J. Applied Math., 34: 157-166.
Elzobi, M. and Z. Lonc, 2003. Partitioning Boolean lattices into antichains. Discrete Math, 260: 45-55.
Direct Link
Greene, C. and D.J. Kleitman, 1978. Proof Techniques in the Theory of Finite Sets, in Studies in Combinatorics. Math Association Amercian, USA., pp: 22-79
Griggs, J.R., 1977. Sufficient conditions for a symmetric chain order. Siam J. Applied Math., 32: 807-809.
Gulminelli, F., P.H. Chomaz and M. Agostino, 2005. Tracking energy fluctuations from fragment partitions in the lattice gas model. Phys. Rev. C, 72: 064618-064618.
Direct Link
Herrman, E., 2001. Infinite chains and antichains in computable partial orderings. J. Symbolic Logic, 66: 923-934.
Direct Link
Rota, G. and T.C. Wallstrom, 1997. Stochastic integrals: A combinatorial approach. Ann. Probabil., 25: 1257-1283.
Sharma, B.D. and M.L. Kaushik, 1986. Algebra of Sharma and Kaushik=s metric inducing partitions of Zq. J. Comb. Inform. Sys. Sci., 11: 19-32.
Simion, R., 1995. On q-analogues of partially ordered sets. J. Combinatorial Theory, Ser. A., 72: 135-183.
Direct Link
Liang, W.H., W.K. Chen and S.Q. Gao, 1990. Applications of lattice theory to graph decomposition. Circuits. Sys. Sign. Process., 9: 181-195.
CrossRef Direct Link
Zaremba, S.K., 1976. On Cartesian products of good lattices. Math. Comput., 30: 546-552.
© Science Alert. All Rights Reserved