共查询到20条相似文献,搜索用时 15 毫秒
1.
Giulio Caviglia 《Journal of Algebraic Combinatorics》2009,30(4):539-548
In this paper we prove that the coordinate ring of the pinched Veronese, k[X
3,X
2
Y,XY
2,Y
3,X
2
Z,Y
2
Z,XZ
2,YZ
2,Z
3], is Koszul. The result is obtained by combining the use of a flat deformation induced by a distinguished weight together
with a generalization of the notion of Koszul filtrations. 相似文献
2.
Let Φ be a finite root system of rank n and let m be a nonnegative integer. The generalized cluster complex Δm(Φ) was introduced by S. Fomin and N. Reading. It was conjectured by these authors that Δm(Φ) is shellable and by V. Reiner that it is (m + 1)-Cohen-Macaulay, in the sense of Baclawski. These statements are proved in this paper. Analogous statements are shown
to hold for the positive part Δ+m(Φ) of Δm(Φ). An explicit homotopy equivalence is given between Δ+m(Φ) and the poset of generalized noncrossing partitions, associated to the pair (Φ, m) by D. Armstrong. 相似文献
3.
Günter M. Ziegler 《Israel Journal of Mathematics》1994,87(1-3):97-110
4.
Bruce E. Sagan 《Order》1986,3(1):47-54
We show that the poset of all partitions of an nd-set with block size divisible by d is shellable. Using similar techniques, it also follows that various other examples of exponential structures cited by Stanley are also shellable. The method used involves the notion of recursive atom orderings introduced by Björner and Wachs.Research supported in part by NATO post-doctoral grant administered by the NSF. 相似文献
5.
An finite interval order is a partially ordered set whose elements are in correspondence with a finite set of intervals in the line, with disjoint intervals being ordered by their relative position. We show that any such order is shellable in the sense that its (not necessarily pure) order complex is shellable. 相似文献
6.
Christos A. Athanasiadis Thomas Brady Colum Watt 《Proceedings of the American Mathematical Society》2007,135(4):939-949
We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type and those of exceptional type and rank at least three.
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Ghorpade Sudhir R. Pratihar Rakhi Randrianarisoa Tovohery H. 《Journal of Algebraic Combinatorics》2022,56(4):1135-1162
Journal of Algebraic Combinatorics - We consider a q-analogue of abstract simplicial complexes, called q-complexes, and discuss the notion of shellability for such complexes. It is shown that... 相似文献
11.
We prove that the Veronese embedding
O
n
(d):
n
N
with n2, d3 does not satisfy property N
p (according to Green and Lazarsfeld) if p3d–2. We make the conjecture that also the converse holds. This is true for n=2 and for n=d=3. 相似文献
12.
N-Free posets have recently taken some importance and motivated many studies. This class of posets introduced by Grillet [8] and Heuchenne [11] are very related to another important class of posets, namely the series-parallel posets, introduced by Lawler [12] and studied by Valdes et al. [21]. This paper shows how N-free posets can be considered as generalizations of series-parallel posets, by giving a recursive construction of N-free posets. Furthermore we propose a linear time algorithm to recognize and decompose any N-free poset. This yields some very naturel problems, namely: which are the properties(such as linear time algorithm for some invariant) of series-parallel posets that are kept for N-free posets? 相似文献
13.
In this paper, we investigate substructures of partially ordered sets which must be present whenever the dimension is large. We show that for eachn1, ifT is a tree onn vertices and ifP is any poset having dimension at least 4n
6, then eitherP or its dual contains the incidence poset ofT as a suborder. 相似文献
14.
The purpose of this paper is to discuss several invariants each of which provides a measure of the intuitive notion of complexity for a finite partially ordered set. For a poset X the invariants discussed include cardinality, width, length, breadth, dimension, weak dimension, interval dimension and semiorder dimension denoted respectively X, W(X), L(X), B(X), dim(X). Wdim(X), Idim(X) and Sdim(X). Among these invariants the following inequalities hold. . We prove that every poset X with three of more points contains a partly with . If M denotes the set of maximal elements and A an arbitrary anticham of X we show that and . We also show that there exist functions f(n,t) and (gt) such that and simply implies . 相似文献
15.
IfM
2 is a nondegenerate surface in a 4-dimensional Riemannian manifold
, then there is a natural affine metricg defined onM
2. It is shown that this affine metricg is conformal to the induced Riemannian metric onM
2 if and only ifM
2 is a minimal submanifold of
in the usual Riemannian sense. If the conformal factor is a constant, then the two metrics are said to be homothetic. It is shown that there does not exist a nondegenerate surface in Euclidean space 4 or hyperbolic spaceH
4 whose affine metric is homothetic to the induced Riemannian metric. Furthermore, ifM
2 is a nondegenerate surface in the standard 4-sphereS
4 whose affine metric is homothetic to the induced Riemannian metric, thenM
2 is a Veronese surface.T. Cecil was supported by NSF Grant No. DMS-9101961. 相似文献
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The reconstruction conjecture for posets is the following: Every finite posetP of more than three elements is uniquely determined — up to isomorphism — by its collection of (unlabelled) one-element-deleted subposets P–{x}:xV(P).We show that disconnected posets, posets with a least (respectively, greatest) element, series decomposable posets, series-parallel posets and interval orders are reconstructible and that N-free orders are recognizable.We show that the following parameters are reconstructible: the number of minimal (respectively, maximal) elements, the level-structure, the ideal-size sequence of the maximal elements, the ideal-size (respectively, filter-size) sequence of any fixed level of the HASSE-diagram and the number of edges of the HASSE-diagram.This is considered to be a first step towards a proof of the reconstruction conjecture for posets.Research partly supported by DAAD. 相似文献
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For a square-free monomial ideal I ? S = k[x 1, x 2,…, x n ], we introduce the notion of quasi-linear quotients. By using the quasi-linear quotients, we give a new algebraic criterion for the shellability of a pure simplicial complex Δ over [n]. Also, we provide a new criterion for the Cohen–Macaulayness of the face ring of a pure simplicial complex Δ. Moreover, we show that the face ring of the spanning simplicial complex (defined in [2]) of an r-cyclic graph is Cohen–Macaulay. 相似文献
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