On Antichains in Product Posets
نویسندگان
چکیده
A corollary of Hilbert’s basis theorem is that any antichain in the set of n-dimensional vectors with non-negative entries is finite. In other words, any antichain in the poset given by cartesian powers of semi-infinite chains is finite. We study several variations of this result. We provide necessary and sufficient conditions for antichains in the cartesian product of posets to be finite or bounded in size. Corresponding results are obtained for the rank-difference of antichains in ranked posets.
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