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61.
Letn andk be arbitrary positive integers,p a prime number and L(k
n)(p) the subgroup lattice of the Abelianp-group (Z/p
k
)
n
. Then there is a positive integerN(n,k) such that whenp
N(n,k),L
(k
N
)(p) has the strong Sperner property. 相似文献
62.
63.
设F_q为q个元素的有限域,q是一个素数的幂.令F_q~((2v))是F_q上的2v维辛空间,M(m,s;2v)表示辛群作用在F_q~((2v))上的子空间的轨道.L(m,s;2v)是M(m,s;2v)的子空间生成的集合.若按照子空间的包含关系来规定L(m,s;2v)的序,则得一偏序集,记为L_O(m,s;2v).本文,首先构造了L(m,s;2v)上的子偏序集L_O(m,s;2v),然后证明这个子偏序集是强一致偏序的.最后利用这个偏序集构造了Leonard对. 相似文献
64.
Relations between generalized effect algebras and the sets of classical and quantum observables endowed with an ordering recently
introduced in [GUDDER, S.: An order for quantum observables, Math. Slovaca 56 (2006), 573–589] are studied. In the classical case, a generalized OMP, while in the quantum case a weak generalized OMP
is obtained. Existence of infima for arbitrary sets and suprema for above bounded sets in the quantum case is shown. Compatibility
in the sense of Mackey is characterized.
This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-032002, grant VEGA 2/3163/23
and Center of excellence SAS, CEPI I/2/2005. 相似文献
65.
A hereditary property of combinatorial structures is a collection of structures (e.g., graphs, posets) which is closed under isomorphism, closed under taking induced substructures (e.g., induced subgraphs), and contains arbitrarily large structures. Given a property , we write for the collection of distinct (i.e., non‐isomorphic) structures in a property with n vertices, and call the function the speed (or unlabeled speed) of . Also, we write for the collection of distinct labeled structures in with vertices labeled , and call the function the labeled speed of . The possible labeled speeds of a hereditary property of graphs have been extensively studied, and the aim of this article is to investigate the possible speeds of other combinatorial structures, namely posets and oriented graphs. More precisely, we show that (for sufficiently large n), the labeled speed of a hereditary property of posets is either 1, or exactly a polynomial, or at least . We also show that there is an initial jump in the possible unlabeled speeds of hereditary properties of posets, tournaments, and directed graphs, from bounded to linear speed, and give a sharp lower bound on the possible linear speeds in each case. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 311–332, 2007 相似文献
66.
Z-Continuous Posets and Their Topological Manifestation 总被引:3,自引:0,他引:3
Marcel Erné 《Applied Categorical Structures》1999,7(1-2):31-70
A subset selection Z assigns to each partially ordered set P a certain collection Z P of subsets. The theory of topological and of algebraic (i.e. finitary) closure spaces extends to the general Z-level, by replacing finite or directed sets, respectively, with arbitrary Z-sets. This leads to a theory of Z-union completeness, Z-arity, Z-soberness etc. Order-theoretical notions such as complete distributivity and continuity of lattices or posets extend to the general Z-setting as well. For example, we characterize Z-distributive posets and Z-continuous posets by certain homomorphism properties and adjunctions. It turns out that for arbitrary subset selections Z, a poset P is strongly Z-continuous iff its Z-join ideal completion Z P is Z-ary and completely distributive. Using that characterization, we show that the category of strongly Z-continuous posets (with interpolation) is concretely isomorphic to the category of Z-ary Z-complete core spaces. For suitable subset selections Y and Z, these are precisely the Y-sober core spaces. 相似文献
67.
Yuichiro Kitajima 《International Journal of Theoretical Physics》2008,47(2):511-519
Hofer-Szabo, Redei and Szabo (Int. J. Theor. Phys. 39:913–919, 2000) defined Reichenbach’s common cause of two correlated events in an orthomodular lattice. In the present paper it is shown
that if logical independent elements in an atomless and complete orthomodular lattice correlate, a common cause of the correlated
elements always exists. 相似文献
68.
广义度量空间和偏序集都具有函数空间.而函数空间的存在为数学构造和计算提供了很大方便.本文还讨论了广义度量空间和偏序集之间的相互转化问题. 相似文献
69.
70.
On the core of ordered submodular cost games 总被引:5,自引:0,他引:5
A general ordertheoretic linear programming model for the study of matroid-type greedy algorithms is introduced. The primal restrictions are given by so-called weakly increasing submodular functions on antichains. The LP-dual is solved by a Monge-type greedy algorithm. The model offers a direct combinatorial explanation for many integrality results in discrete optimization. In particular, the submodular intersection theorem of Edmonds and Giles is seen to extend to the case with a rooted forest as underlying structure. The core of associated polyhedra is introduced and applications to the existence of the core in cooperative game theory are discussed. Received: November 2, 1995 / Accepted: September 15, 1999?Published online February 23, 2000 相似文献