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41.
We provide a generalization of pseudo-Frobenius numbers of numerical semigroups to the context of the simplicial affine semigroups. In this way, we characterize the Cohen-Macaulay type of the simplicial affine semigroup ring . We define the type of S, , in terms of some Apéry sets of S and show that it coincides with the Cohen-Macaulay type of the semigroup ring, when is Cohen-Macaulay. If is a d-dimensional Cohen-Macaulay ring of embedding dimension at most , then . Otherwise, might be arbitrary large and it has no upper bound in terms of the embedding dimension. Finally, we present a generating set for the conductor of S as an ideal of its normalization. 相似文献
42.
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
43.
《Annals of Pure and Applied Logic》2020,171(9):102845
A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented by generators and relations. 相似文献
44.
45.
Kelly T. Au 《Mathematical Programming》1996,72(3):259-272
For optimization problems with computationally demanding objective functions and subgradients, inexact subgradient methods
(IXS) have been introduced by using successive approximation schemes within subgradient optimization methods (Au et al., 1994).
In this paper, we develop alternative solution procedures when the primal-dual information of IXS is utilized. This approach
is especially useful when the projection operation onto the feasible set is difficult. We also demonstrate its applicability
to stochastic linear programs. 相似文献
46.
Hiroshi Maeda 《Advances in Mathematics》2007,212(2):458-483
For several important classes of manifolds acted on by the torus, the information about the action can be encoded combinatorially by a regular n-valent graph with vector labels on its edges, which we refer to as the torus graph. By analogy with the GKM-graphs, we introduce the notion of equivariant cohomology of a torus graph, and show that it is isomorphic to the face ring of the associated simplicial poset. This extends a series of previous results on the equivariant cohomology of torus manifolds. As a primary combinatorial application, we show that a simplicial poset is Cohen-Macaulay if its face ring is Cohen-Macaulay. This completes the algebraic characterisation of Cohen-Macaulay posets initiated by Stanley. We also study blow-ups of torus graphs and manifolds from both the algebraic and the topological points of view. 相似文献
47.
Jason Bell 《Discrete Mathematics》2007,307(6):668-682
We show that each polynomial a(z)=1+a1z+?+adzd in N[z] having only real zeros is the f-polynomial of a multicomplex. It follows that a(z) is also the h-polynomial of a Cohen-Macaulay ring and is the g-polynomial of a simplicial polytope. We conjecture that a(z) is also the f-polynomial of a simplicial complex and show that the multicomplex result implies this in the special case that the zeros of a(z) belong to the real interval [-1,0). We also show that for fixed d the conjecture can fail for at most finitely many polynomials having the required form. 相似文献
48.
Elias Gabriel Minian 《K-Theory》2006,37(3):249-261
We show how to construct a categorical spectrum of small categories, and hence a cohomology theory, starting from a Γ-category.
This extends Segal’s infinite loop space machine for topological spaces to small categories. Our results form a part of Bak’s
program for delooping global actions, global categories, and related objects. 相似文献
49.
Jørgen E. Harmse 《Journal of Mathematical Analysis and Applications》2008,339(1):429-437
It is natural to conjecture that if a function f is continuous on the closed region determined by a rectifiable 1-cycle Γ and complex-differentiable on the open region then Γ∫f=0. The main result is an extension of the classical Cauchy-Goursat Theorem: the equality conjectured holds (with no boundary condition on f′) under the additional hypothesis that the winding numbers of Γ define an Lp function and f satisfies a matching Hölder continuity condition near the image of Γ. (In particular, continuity suffices if p=∞.) The proof uses approximations of a rectifiable path by piecewise linear paths. 相似文献
50.
We describe a Cat-valued nerve of bicategories, which associates to every bicategory a simplicial object in Cat, called the 2-nerve. This becomes the object part of a 2-functor N : NHom → [Δop,Cat], where NHom is a 2-category whose objects are bicategories and whose 1-cells are normal homomorphisms of bicategories. The 2-functor
N is fully faithful and has a left biadjoint, and we characterize its image. The 2-nerve of a bicategory is always a weak 2-category
in the sense of Tamsamani, and we show that NHom is biequivalent to a certain 2-category whose objects are Tamsamani weak 2-categories.
The hospitality of Macquarie University and the support of the Australian Research Council are gratefully acknowledged by
S. Lack.
The support of the Australian Research Council is gratefully acknowledged by S. Paoli. 相似文献