• 제목/요약/키워드: bipartite ordered set

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THE DIMENSION OF THE CONVOLUTION OF BIPARTITE ORDERED SETS

  • Bae, Deok-Rak
    • 대한수학회지
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    • 제36권3호
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    • pp.633-648
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    • 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.

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