Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

THE DIMENSION OF THE RECTANGULAR PRODUCT OF LATTICES

  • Published : 1999.01.01
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Abstract

In this paper, we determine the dimension of the rectangular product of certain finite lattices. In face, if L1 and a L2 be finite lattices which satisfy the some conditions, then we have dim (L1$\square$L2) = dim(L1) + dim(L2) - 1.

Keywords

References

  1. Dimension, join-independence and breadth in partially ordered sets K. A. Baker
  2. Discrete Math. v.79 Rectangular products of lattices M. K. Bennett
  3. Amer. Math. Soc. v.63 Partially ordered sets B. Dushnik;E. Miller
  4. Sci. Rep. Kanazawa. Univ. v.4 On the dimension of partially ordered sets Hiraguchi
  5. Discrete Math. v.35 On the dimension of partially ordered sets D. Kelly
  6. Discrete Math. v.88 The dimension of the Cartesian product of posets C. Lin
  7. Amer. Math. Soc. Colloq. Pub. v.38 Theory of graphs O. Ore
  8. Discrete Math. v.25 The Rnak of Distributive Lattice I. Rabinovitch;I. Rival
  9. Order v.6 On the dimension of the Cartesian product of relation and orders K. Reuter
  10. Fund. Math. v.16 Sur l'extension de l'ordre partiel E. Szpilajn
  11. Discrete Math. v.53 The dimension of the Cartesian product of partial orders W. T. Trotter
  12. Order v.2 Tensorial Decomposition of Concept Lattices R. Wille