منابع مشابه
On Poset Boolean Algebras
Let 〈P,≤〉 be a partially ordered set. We define the poset Boolean algebra of P , and denote it by F (P ). The set of generators of F (P ) is {xp : p ∈ P}, and the set of relations is {xp ·xq = xp : p ≤ q}. We say that a Boolean algebra B is well-generated, if B has a sublattice G such that G generates B and 〈G,≤G〉 is well-founded. A wellgenerated algebra is superatomic. Theorem 1 Let 〈P,≤〉 be a...
متن کاملTail and free poset algebras
We characterize free poset algebras F (P ) over partially ordered sets and show that they can be represented by upper semi-lattice algebras. Hence, the uniqueness, in decomposition into normal form, using symmetric difference, of non-zero elements of F (P ) is established. Moreover, a characterization of upper semilattice algebras that are isomorphic to free poset algebras is given in terms of ...
متن کاملPoset algebras over well quasi-ordered posets
A new class of partial order-types, class G bqo is defined and investigated here. A poset P is in the class G bqo iff the poset algebra F (P ) is generated by a better quasi-order G that is included in L(P ). The free Boolean algebra F (P ) and its free distrivutive lattice L(P ) were defined in [ABKR]. The free Boolean algebra F (P ) contains the partial order P and is generated by it: F (P ) ...
متن کاملSome Basics on Tolerances
In this paper we deal with sensitivity analysis of combinatorial optimization problems and its fundamental term, the tolerance. For three classes of objective functions (Σ,Π,MAX) we give some basic properties on upper and lower tolerances. We show that the upper tolerance of an element is well defined, how to compute the upper tolerance of an element, and give equivalent formulations when the u...
متن کاملOn Poset Merging∗
We consider the follow poset merging problem: Let X and Y be two subsets of a partially ordered set S. Given complete information about the ordering within both X and Y , how many comparisons are needed to determine the order on X ∪ Y ? This problem is a natural generalization of the list merging problem. While searching in partially ordered sets and sorting partially ordered sets have been con...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 1992
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.1992.126238