The Dimension of the Convolution of Bipartite Ordered Sets
نویسنده
چکیده
In this paper, for any two bipartite ordered sets P and Q; we de ne 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-min integer of the certain realizers. In particular, we also prove that dim(Pn;k) = n+k b n+k 3 c 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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