On the well dimension of ordered sets
نویسندگان
چکیده
منابع مشابه
The Dimension of Random Ordered Sets
Let P = (X, <) be a finite ordered set and let I PI denote the cardinality of the universe X. Also let A(P) denote the maximum degree of P, i.e., the maximum number of points comparable to any one point of P. Fiiredi and Kahn used probabilistic methods to show that the dimension of P satisfies dim(P) I c,A(P) log(P1 and dim(P) 5 c,A(P) log2A(P) where c , and c, are positive absolute constants. ...
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We consider conditions which force a well-quasi-ordered poset (wqo) to be betterquasi-ordered (bqo). In particular we obtain that if a poset P is wqo and the set Sω(P ) of strictly increasing sequences of elements of P is bqo under domination, then P is bqo. As a consequence, we get the same conclusion if Sω(P ) is replaced by J (P ), the collection of non-principal ideals of P , or by AM(P ), ...
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We use a variety of combinatorial techniques to prove several theorems concerning fractional dimension of partially ordered sets. In particular, we settle a conjecture of Brightwell and Scheinerman by showing that the fractional dimension of a poset is never more than the maximum degree plus one. Furthermore, when the maximum degree k is at least two, we show that equality holds if and only if ...
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It is known that the \pattern containment" order on permutations is not a partial well-order. Nevertheless, many naturally de ned subsets of permutations are partially well-ordered, in which case they have a strong nite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains are exhibited that give some insight as...
متن کاملThe Dimension of the Convolution of Bipartite Ordered Sets
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 stand...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1969
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1969.100871