共查询到20条相似文献,搜索用时 482 毫秒
1.
Catherine Stenson 《Discrete and Computational Geometry》2005,34(3):507-521
We use the Billera-Liu algebra to show how the flag f-vectors of several special
classes of polytopes fit into the closed convex hull of the flag f-vectors
of all polytopes. In particular, we describe inequalities that define the faces of
the closed convex hull of the flag f-vectors of all d-polytopes that are spanned
by the flag f-vectors of simplicial, simple, k-simplicial, and k-simple d-polytopes. We also describe inequalities that define the face of the closed convex hull of the flag f-vectors of all d-zonotopes spanned by the flag f-vectors of cubical d-zonotopes, and give an upper bound on the dimension of the span of the flag f-vectors of k-cubical zonotopes. Finally, we strengthen some previously known inequalities for flag f-vectors of zonotopes. 相似文献
2.
We describe a new technique for constructing convex polytopes—a generalization of Shemer’s sewing construction for simplicial
neighborly polytopes that has been modified to allow the creation of nonsimplicial polytopes as well. We show that Bisztriczky’s
ordinary polytopes can be constructed in this manner, and we also construct several infinite families of polytopes. We consider
bounds on the flag f-vectors of 4-polytopes that can be inductively constructed by generalized sewing starting from the 4-simplex. 相似文献
3.
Richard Ehrenborg 《Advances in Mathematics》2005,193(1):205-222
We present a method of lifting linear inequalities for the flag f-vector of polytopes to higher dimensions. Known inequalities that can be lifted using this technique are the non-negativity of the toric g-vector and that the simplex minimizes the cd-index. We obtain new inequalities for six-dimensional polytopes. In the last section we present the currently best known inequalities for dimensions 5 through 8. 相似文献
4.
The recursive nature of cominuscule Schubert calculus 总被引:1,自引:0,他引:1
The necessary and sufficient Horn inequalities which determine the non-vanishing Littlewood-Richardson coefficients in the cohomology of a Grassmannian are recursive in that they are naturally indexed by non-vanishing Littlewood-Richardson coefficients on smaller Grassmannians. We show how non-vanishing in the Schubert calculus for cominuscule flag varieties is similarly recursive. For these varieties, the non-vanishing of products of Schubert classes is controlled by the non-vanishing products on smaller cominuscule flag varieties. In particular, we show that the lists of Schubert classes whose product is non-zero naturally correspond to the integer points in the feasibility polytope, which is defined by inequalities coming from non-vanishing products of Schubert classes on smaller cominuscule flag varieties. While the Grassmannian is cominuscule, our necessary and sufficient inequalities are different than the classical Horn inequalities. 相似文献
5.
The flag Whitney numbers (also referred to as the flag f-numbers)
of a geometric lattice count the number of
chains of the lattice with elements having specified ranks.
We give a collection of inequalities which imply all the linear
inequalities satisfied by the flag Whitney numbers of rank 3
geometric lattices. We further describe the smallest closed convex
set containing the flag Whitney numbers of rank 3 geometric lattices
as well as the smallest closed convex set containing the flag Whitney
numbers of those lattices
corresponding to oriented matroids. 相似文献
6.
Natalie Aisbett 《Discrete and Computational Geometry》2014,51(2):323-336
For any flag nestohedron, we define a flag simplicial complex whose f-vector is the γ-vector of the nestohedron. This proves that the γ-vector of any flag nestohedron satisfies the Frankl–Füredi–Kalai inequalities, partially solving a conjecture by Nevo and Petersen (Discrete Comput. Geom. 45:503–521, 2010). We also compare these complexes to those defined by Nevo and Petersen (Discrete Comput. Geom. 45:503–521, 2010) for particular flag nestohedra. 相似文献
7.
We present examples of flag homology spheres whose γ-vectors satisfy the Kruskal–Katona inequalities. This includes several families of well-studied simplicial complexes, including
Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In these cases, we construct
explicit flag simplicial complexes whose f-vectors are the γ-vectors in question, and so a result of Frohmader shows that the γ-vectors satisfy not only the Kruskal–Katona inequalities but also the stronger Frankl–Füredi–Kalai inequalities. In another
direction, we show that if a flag (d−1)-sphere has at most 2d+3 vertices its γ-vector satisfies the Frankl–Füredi–Kalai inequalities. We conjecture that if Δ is a flag homology sphere then γ(Δ) satisfies the Kruskal–Katona, and further, the Frankl–Füredi–Kalai inequalities. This conjecture is a significant refinement
of Gal’s conjecture, which asserts that such γ-vectors are nonnegative. 相似文献
8.
Carl W. Lee 《Israel Journal of Mathematics》1984,47(4):261-269
Letf(P
s
d
) be the set of allf-vectors of simpliciald-polytopes. ForP a simplicial 2d-polytope let Σ(P) denote the boundary complex ofP. We show that for eachf ∈f(P
s
d
) there is a simpliciald-polytopeP withf(P)=f such that the 11 02 simplicial diameter of Σ(P) is no more thanf
0(P)−d+1 (one greater than the conjectured Hirsch bound) and thatP admits a subdivision into a simpliciald-ball with no new vertices that satisfies the Hirsch property. Further, we demonstrate that the number of bistellar operations
required to obtain Σ(P) from the boundary of ad-simplex is minimum over the class of all simplicial polytopes with the samef-vector. This polytopeP will be the one constructed to prove the sufficiency of McMullen's conditions forf-vectors of simplicial polytopes. 相似文献
9.
Shawn Austin Walker 《Combinatorica》2007,27(4):489-501
Suppose that C is a balanced simplicial complex. We show that its flag f-vector contains an interesting multiplicative structure. We define η
s
(C):= log2
f
S
(C), and characterize the convex cone in which this flag η-vector may lie. Additionally, we specialize our results to the case when C is a pure balanced simplicial complex, and when C is a graded poset. 相似文献
10.
We study degree sequences for simplicial posets and polyhedral complexes, generalizing the well-studied graphical degree sequences. Here we extend the more common generalization of vertex-to-facet degree sequences by considering arbitrary face-to-flag degree sequences. In particular, these may be viewed as natural refinements of the flag f-vector of the poset. We investigate properties and relations of these generalized degree sequences, proving linear relations between flag degree sequences in terms of the composition of rank jumps of the flag. As a corollary, we recover an f-vector inequality on simplicial posets first shown by Stanley. 相似文献
11.
We obtain exact constants in Jackson-type inequalities for smoothness characteristics Λk(f), k ∈ N, defined by averaging the kth-order finite differences of functions f ∈ L2. On the basis of this, for differentiable functions in the classes L2r, r ∈ N, we refine the constants in Jackson-type inequalities containing the kth-order modulus of continuity ωk. For classes of functions defined by their smoothness characteristics Λk(f) and majorants Φ satisfying a number of conditions, we calculate the exact values of certain n-widths. 相似文献
12.
Rafael Gillmann 《Journal of Combinatorial Theory, Series A》2006,113(5):799-821
We introduce revlex-initial 0/1-polytopes as the convex hulls of reverse-lexicographically initial subsets of 0/1-vectors. These polytopes are special knapsack-polytopes. It turns out that they have remarkable extremal properties. In particular, we use these polytopes in order to prove that the minimum numbers gnfac(d,n) of facets and the minimum average degree gavdeg(d,n) of the graph of a d-dimensional 0/1-polytope with n vertices satisfy gnfac(d,n)?3d and gavdeg(d,n)?d+4. We furthermore show that, despite the sparsity of their graphs, revlex-initial 0/1-polytopes satisfy a conjecture due to Mihail and Vazirani, claiming that the graphs of 0/1-polytopes have edge-expansion at least one. 相似文献
13.
It is shown that if three vertices of the graph G(l') of a convex 3-polytope P are chosen, then G(P) contains a refinement of the complete graph C4 on four vertices, for which the three chosen vertices are principal (that is, correspond to vertices of C4 in the refinement). In general, all four vertices may not be preassigned as principal. For dimensions d?4, simple (simplicial) d-polytopes are constructed whose graphs contain sets of three (four) vertices, which cannot all be principal in any refinement of C4+1. 相似文献
14.
We prove weighted strong inequalities for the multilinear potential operator Tf{\cal T}_{\phi} and its commutator, where the kernel ϕ satisfies certain growth condition. For these operators we also obtain Fefferman-Stein type inequalities and Coifman type
estimates. Moreover we prove weighted weak type inequalities for the multilinear maximal operator Mj,LB\mathcal{M}_{\varphi,L^{B}} associated to an essentially nondecreasing function φ and to the Orlicz space L
B
for a given Young function B. This result allows us to obtain a weighted weak type inequality for the operator Tf{\cal T}_{\phi}. 相似文献
15.
Transcendence measures and algebraic growth of entire functions 总被引:1,自引:1,他引:0
In this paper we obtain estimates for certain transcendence measures of an entire function f. Using these estimates, we prove Bernstein, doubling and Markov inequalities for a polynomial P(z,w) in ℂ2 along the graph of f. These inequalities provide, in turn, estimates for the number of zeros of the function P(z,f(z)) in the disk of radius r, in terms of the degree of P and of r.
Our estimates hold for arbitrary entire functions f of finite order, and for a subsequence {n
j
} of degrees of polynomials. But for special classes of functions, including the Riemann ζ-function, they hold for all degrees
and are asymptotically best possible. From this theory we derive lower estimates for a certain algebraic measure of a set
of values f(E), in terms of the size of the set E. 相似文献
16.
D. A. Kirillova 《Russian Mathematics (Iz VUZ)》2010,54(9):74-76
In this paper we establish inequalities involving moduli of derivatives |f′
k
(0)| of functions f
k
univalent in the unit disk |z| < 1 having no common values and translating zero into a point on the segment [−1, 1], k = 1, …, n. We estimate f
k
by means of Schwarzian derivatives. 相似文献
17.
In this paper, a boundary version of the Schwarz inequality is investigated. We obtain more general results at the boundary. If we know the second coefficient in the expansion of the function f(z) = 1 + cpzp + cp + 1zp + 1…, then we obtain new inequalities of the Schwarz inequality at boundary by taking into account cp + 1 and zeros of the function f(z) ? 1. The sharpness of these inequalities is also proved. 相似文献
18.
R. Ehrenborg D. Johnston R. Rajagopalan M. Readdy 《Discrete and Computational Geometry》2000,23(2):261-271
We show how the flag f -vector of a polytope changes when cutting off any face, generalizing work of Lee for simple polytopes. The result is in
terms of explicit linear operators on cd-polynomials. Also, we obtain the change in the flag f -vector when contracting any face of the polytope.
Received July 13, 1998, and in revised form April 14, 1999. 相似文献
19.
Gil Kalai 《Israel Journal of Mathematics》1984,48(2-3):175-195
LetK=K
1,...,Kn be a family ofn convex sets inR
d
. For 0≦i<n denote byf
i the number of subfamilies ofK of sizei+1 with non-empty intersection. The vectorf(K) is called thef-vectors ofK. In 1973 Eckhoff proposed a characterization of the set off-vectors of finite families of convex sets inR
d
by a system of inequalities. Here we prove the necessity of Eckhoff's inequalities. The proof uses exterior algebra techniques.
We introduce a notion of generalized homology groups for simplicial complexes. These groups play a crucial role in the proof,
and may be of some independent interest. 相似文献
20.
We obtain sharp Jackson-Stechkin type inequalities for moduli of continuity of kth order Ω k in which, instead of the shift operator T h f, the Steklov operator S h (f) is used. Similar smoothness characteristic of functions were studied earlier in papers of Abilov, Abilova, Kokilashvili, and others. For classes of functions defined by these characteristics, we calculate the exact values of certain n-widths. 相似文献