• Title/Summary/Keyword: Ferrers dimension

Search Result 3, Processing Time 0.014 seconds

THE DIMENSION OF THE RECTANGULAR PRODUCT OF LATTICES

  • Bae, Deok-Rak
    • Journal of the Korean Mathematical Society
    • /
    • v.36 no.1
    • /
    • pp.15-36
    • /
    • 1999
  • 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.

  • PDF

THE DIMENSION OF THE CONVOLUTION OF BIPARTITE ORDERED SETS

  • Bae, Deok-Rak
    • Journal of the Korean Mathematical Society
    • /
    • v.36 no.3
    • /
    • pp.633-648
    • /
    • 1999
  • In this paper, for any two bipartite ordered sets P and Q, we define the convolution P * Q of P and Q. For dim(P)=s and dim(Q)=t, we prove that s+t-(U+V)-2 dim(P*Q) s+t-(U+V)+2, where U+V is the max-mn integer of the certain realizers. In particular, we also prove that dim(P)=n+k- {{{{ { n+k} over {3 } }}}} for 2 k n<2k and dim(Pn ,k)=n for n 2k, where Pn,k=Sn*Sk is the convolution of two standard ordered sets Sn and Sk.

  • PDF