منابع مشابه
Orbits of Antichains in Certain Root Posets
Building everything from scratch, we give another proof of Propp and Roby’s theorem saying that the average antichain size in any reverse operator orbit of the poset [m] × [n] is mn m+n . It is conceivable that our method should work for other situations. As a demonstration, we show that the average size of antichains in any reverse operator orbit of [m] ×Kn−1 equals 2mn m+2n−1 . Here Kn−1 is t...
متن کاملOn Antichains in Product Posets
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 bo...
متن کاملOptimal antichains and ideals in Macaulay posets
A ranked poset P is a Macaulay poset if there exists a linear ordering of its elements such that for any i and any subset F of the i{th level N i the shadow of the jFj smallest elements of N i w.r.t. is contained in the set of the smallest j(F)j elements of N i?1 , where (F) denotes the shadow of F. We consider the following three optimization problems for P : (i) Find the maximum weight of an ...
متن کاملOn orbits of antichains of positive roots
For any finite poset P, there is a natural operator, X = XP, acting on the set of antichains of P. We discuss conjectural properties of X for some graded posets associated with irreducible root systems. In particular, if ∆ is the set of positive roots and Π is the set of simple roots in ∆, then we consider the cases P = ∆ and P = ∆ \ Π. For the root system of type An, we consider an X-invariant...
متن کاملThe Number of Linear Extensions of Ranked Posets
We revisit the question of counting the number of linear extensions of the Boolean lattice, relating this to the polyhedral methods of Kahn and Kim, and of Stanley. We give simpler proofs of various known results, and give an upper bound on the number of linear extensions of an arbitrary ranked poset satisfying the LYM condition. [Note: This preprint is not intended for journal publication, as ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1993
ISSN: 0195-6698
DOI: 10.1006/eujc.1993.1003