대한수학회지 (Journal of the Korean Mathematical Society)

  • 제36권3호
  • /
  • Pages.633-648
  • /
  • 1999
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

THE DIMENSION OF THE CONVOLUTION OF BIPARTITE ORDERED SETS

  • 발행 : 1999.03.01
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초록

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.

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참고문헌

  1. Dimension and interval dimension of certain bipartite ordered sets no.SUP. D. R. Bae;J. G. Lee
  2. Amer. Math. Soc. v.63 Partially ordered sets B. Dushnik;E. Miller
  3. Fund. Math. v.16 Sur I'extension de I'ordre partiel E. Szpilrajn
  4. Unpublished manuscript On the construction of irreducible partially ordered sets W. T. Trotter
  5. Disc. Math. v.35 Stacks and splits of partially ordered sets W. T. Trotter
  6. Combinatorics and Partially Ordered Sets; Dimension Theory W. T. Trotter
  7. Tensorial decomposition of concept lattices, order v.2 R. Wille