共查询到20条相似文献,搜索用时 11 毫秒
1.
A theorem of N. Terai and T. Hibi for finite distributive lattices and a theorem of Hibi for finite modular lattices (suggested by R.P. Stanley) are equivalent to the following: if a finite distributive or modular lattice of rank d contains a complemented rank 3 interval, then the lattice is (d+1)-connected.In this paper, the following generalization is proved: Let L be a (finite or infinite) semimodular lattice of rank d that is not a chain (d∈N0). Then the comparability graph of L is (d+1)-connected if and only if L has no simplicial elements, where z∈L is simplicial if the elements comparable to z form a chain. 相似文献
2.
The probability that m randomly chosen elements
of a finite power associative loop
have prescribed orders and generate
is calculated in terms of certain constants
related to the action of Aut(
) on the subloop lattice of
. As an illustration, all meaningful
probabilities of random generation by elements of given orders are found for the smallest
nonassociative simple Moufang loop. 相似文献
3.
Joseph P. S. Kung 《Order》1985,2(2):105-112
An element in a lattice is join-irreducible if x=ab implies x=a or x=b. A meet-irreducible is a join-irreducible in the order dual. A lattice is consistent if for every element x and every join-irreducible j, the element xj is a join-irreducible in the upper interval [x, î]. We prove that in a finite consistent lattice, the incidence matrix of meet-irreducibles versus join-irreducibles has rank the number of join-irreducibles. Since modular lattices and their order duals are consistent, this settles a conjecture of Rival on matchings in modular lattices. 相似文献
4.
Lattices in the variety
of lower bounded lattices of rank k are characterized. A sufficient condition for a lattice to be lower bounded is given, and used to produce a new example of a non-finitely-generated lower bounded lattice. Lattices that are subdirect products of finite lower bounded lattices are characterized.In memory of Ivan RivalReceived September 18, 2003; accepted in final form October 5, 2004.This revised version was published online in August 2005 with a corrected cover date. 相似文献
5.
David Robert Wasserman 《Algebra Universalis》2006,55(1):67-84
We use dominions to show that many varieties of lattices have nonsurjective epimorphisms. The variety D of distributive lattices is treated in detail. We show that the dominion in D of a sublattice
is the closure of M under relative complementation in L. This dominion is also the largest sublattice of L in which M is epimorphically embedded. In any variety of lattices larger than D, the dominion of M in L is just M.
Received May 1, 2001; accepted in final form October 4, 2005. 相似文献
6.
We construct posets of dimension 2 with highly chromatic Hasse diagrams. This solves a previous problem by Nesetril and Trotter. 相似文献
7.
In the view-obstruction problem, congruent, closed convex bodies centred at the points
in
n
are expanded uniformly until they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1 and cubes of side 1 these values are known forn=2, 3 and 4. Here we show that in 5, this value for the sphere of diameter 1 is
. 相似文献
8.
We prove that there is no free object over a countable set in the category of complete distributive lattices with homomorphisms preserving binary meets and arbitrary joins. 相似文献
9.
Klaus Reuter 《Order》1985,1(3):265-276
A tolerance relation of a lattice L, i.e., a reflexive and symmetric relation of L which is compatible with join and meet, is called glued if covering blocks of have nonempty intersection. For a lattice L with a glued tolerance relation we prove a formula counting the number of elements of L with exactly k lower (upper) covers. Moreover, we prove similar formulas for incidence structures and graphs and we give a new proof of Dilworth's covering theorem. 相似文献
10.
11.
Winfried Geyer 《Order》1993,10(4):363-373
In this paper, we consider the following reconstruction problem: Given two ordered sets (G, ) and (M, ) representing join- and meet-irreducible elements, respectively together with three relationsJ,,
onG×M modelling comparability (gm) and maximal noncomparability with respect tog (gm, butgm*) and with respect tom (gm, butgm*). We determine necessary and sufficient conditions for the existence of a finite latticeL and injections :GJ(L) and :MM(L) such that the given order relations and the abstract relations coincide with the one induced by the latticeL. 相似文献
12.
Yevhen Zelenyuk 《Topology and its Applications》2011,158(9):1172-1178
The pseudo-intersection number, denoted p, is the minimum cardinality of a family A⊆P(ω) having the strong finite intersection property but no infinite pseudo-intersection. For every countable topologizable group G, let pG denote the minimum character of a nondiscrete Hausdorff group topology on G which cannot be refined to a nondiscrete metrizable group topology. We show that pG=p. 相似文献
13.
Thefunction lattice L
P is the lattice of all isotone maps from a posetP into a latticeL.D. Duffus, B. Jónsson, and I. Rival proved in 1978 that for afinite poset P, the congruence lattice ofL
P is a direct power of the congruence lattice ofL; the exponent is |P|.This result fails for infiniteP. However, utilizing a generalization of theL
P construction, theL[D] construction (the extension ofL byD, whereD is a bounded distributive lattice), the second author proved in 1979 that ConL[D] is isomorphic to (ConL) [ConD] for afinite lattice L.In this paper we prove that the isomorphism ConL[D](ConL)[ConD] holds for a latticeL and a bounded distributive latticeD iff either ConL orD is finite.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903. 相似文献
14.
A tensor product for complete lattices is studied via concept lattices. A characterization as a universal solution and an ideal representation of the tensor products are given. In a large class of concept lattices which contains all finite ones, the subdirect decompositions of a tensor product can be determined by the subdirect decompositions of its factors. As a consequence, one obtains that the tensor product of completely subdirectly irreducible concept lattices of this class is again completely subdirectly irreducible. Finally, applications to conceptual measurement are discussed.Dedicated to Ernst-August Behrens on the occasion of his seventieth birthday. 相似文献
15.
Kevin?Ford 《Combinatorica》2003,23(2):263-281
Let N
t
(k) be the maximum number of
k-term arithmetic
progressions of real numbers, any two of which have
t points in common. We
determine N
2(k) for prime k and all large k, and give upper and lower bounds for
N
t
(k) when t 3.* Research supported in part by NSF grant
DMS-0070618. 相似文献
16.
Summary An equational identity of a given type involves two kinds of symbols: individual variables and the operation symbols. For example, the distributive identity: x (y + z) = x y + x z has three variable symbols {x, y, z} and two operation symbols {+, }. Here the variables range over all the elements of the base set while the two operation symbols are fixed. However, we shall say that an identity ishypersatisfied by a varietyV if, whenever we also allow the operation symbols to range over all polynomials of appropriate arity, the resulting identities are all satisfied byV in the usual sense. For example, the ring of integers Z; +, satisfies the above distributive law, but it does not hypersatisfy the same formal law because, e.g., the identityx + (y z) = (x + y) (x + z) is not valid. By contrast, is hypersatisfied by the variety of all distributive lattices and is thus referred to as a distributive latticehyperidentity. Thus a hyperidentity may be viewed as an equational scheme for writing a class of identities of a given type and the original identities themselves are obtained as special cases by substituting specific polynomials of appropriate arity for the operation symbols in the scheme. In this paper, we provide afinite equational scheme which is a basis for the set of all binary lattice hyperidentities of type 2, 2, .This research was supported by the NSERC operating grant # 8215 相似文献
17.
A. Krzysztof Kwaśniewski 《Advances in Applied Clifford Algebras》2008,18(1):57-73
We introduce a natural partial order ≤ in structurally natural finite subsets of the cobweb prefabs sets recently constructed
by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling-like numbers’
triangular array — are then calculated and the explicit formula for them is provided. Next — in the second construction —
we endow the set sums of prefabiants with such an another partial order that their Bell-like numbers include Fibonacci triad
sequences introduced recently by the present author in order to extend famous relation between binomial Newton coefficients
and Fibonacci numbers onto the infinity of their relatives among whom there are also the Fibonacci triad sequences and binomial-like
coefficients (incidence coefficients included). The first partial order is F-sequence independent while the second partial order is F-sequence dependent where F is the so-called admissible sequence determining cobweb poset by construction. An F-determined cobweb poset’s Hasse diagram becomes Fibonacci tree sheathed with specific cobweb if the sequence F is chosen to be just the Fibonacci sequence. From the stand-point of linear algebra of formal series these are generating
functions which stay for the so-called extended coherent states of quantum physics. This information is delivered in the last
section.
Presentation (November 2006) at the Gian-Carlo Rota Polish Seminar . 相似文献
18.
Huberta Lausch 《Geometriae Dedicata》1995,56(2):121-127
All normal subloops of a loopG form a modular latticeL
n
(G). It is shown that a finite loopG has a complemented normal subloop lattice if and only ifG is a direct product of simple subloops. In particular,L
n
(G) is a Boolean algebra if and only if no two isomorphic factors occurring in a decomposition ofG are abelian groups. The normal subloop lattice of a finite loop is a projective geometry if and only ifG is an elementary abelianp-group for some primep. 相似文献
19.
Jörg Stephan 《Order》1993,10(2):133-142
Some relations between the classB of lattices of breadth at most two and its subclassD of dismantlable lattices, as well as the lattice varietiesV (B) andV (D) generated byV (D) andV (D), respectively, are studied in this paper. For finite join-semidistributive lattices, the two concepts of dismantlability and breadth at most two coincide. There are infinitely many lattice varieties between the varietiesV (D) andV (B), none of them is finitely based. 相似文献
20.
We describe the free modular lattice generated by two chains and a single point, under the assumption that there are few meets.
Received February 11, 2005; accepted in final form August 11, 2005. 相似文献