منابع مشابه
The number of tiered posets modulo six
Our goal in this note is to sketch a proof of a conjecture made by Kreweras [1] in a paper published in this journal. A poset on an n-set is said to be tiered with height h if every element belongs to a maximal chain with exactly h elements. It is easy to visualize these posets in terms of their Hasse diagrams. The elements can be arranged in tiers with the minimal elements in the first tier an...
متن کاملInterval number of special posets and random posets
The interval number i(P) of a poset P is the smallest t such that P is a containment of sets that are unions of at most t real intervals. For the special poset Bn(k) consisting of the singletons and ksubsets of an n-element set, ordered by inclusion, i(Bn(k)) = min {k, n − k + 1} if |n/2 − k | ≥ n/2 − (n/2). For bipartite posets with n elements or n minimal elements, i(P) ≤ n lgn − lglgn + ...
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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In recent years, researchers have shown renewed interest in combinatorial properties of posets determined by geometric properties of its order diagram and topological properties of its cover graph. In most cases, the roots for the problems being studied today can be traced back to the 1970’s, and sometimes even earlier. In this paper, we study the problem of bounding the dimension of a planar p...
متن کاملSubsets of Posets Minimising the Number of Chains
A well-known theorem of Sperner describes the largest collections of subsets of an nelement set none of which contains another set from the collection. Generalising this result, Erdős characterised the largest families of subsets of an n-element set that do not contain a chain of sets A1 ⊂ . . . ⊂ Ak of an arbitrary length k. The extremal families contain all subsets whose cardinalities belong ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1986
ISSN: 0012-365X
DOI: 10.1016/0012-365x(86)90216-5