共查询到20条相似文献,搜索用时 31 毫秒
1.
We disclaim Conjecture 1 posed by Seifter in [N. Seifter, Transitive digraphs with more than one end, Discrete Math., to appear], that stated that a connected locally finite digraph with more than one end is either 0-, 1- or highly arc transitive. We describe in this work an infinite family of 2-arc transitive two-ended digraphs, that are not 3-arc transitive. 相似文献
2.
Arthur Bartels 《Advances in Mathematics》2007,209(1):337-362
We introduce the Farrell-Jones Conjecture with coefficients in an additive category with G-action. This is a variant of the Farrell-Jones Conjecture about the algebraic K- or L-theory of a group ring RG. It allows to treat twisted group rings and crossed product rings. The conjecture with coefficients is stronger than the original conjecture but it has better inheritance properties. Since known proofs using controlled algebra carry over to the set-up with coefficients we obtain new results about the original Farrell-Jones Conjecture. The conjecture with coefficients implies the fibered version of the Farrell-Jones Conjecture. 相似文献
3.
4.
Duško Jojić Siniša T. Vrećica Rade T. Živaljević 《Journal of Algebraic Combinatorics》2017,46(1):15-31
We prove a new theorem of Tverberg–van Kampen–Flores type, which confirms a conjecture of Blagojevi? et al. about the existence of ‘balanced Tverberg partitions’ (Conjecture 6.6 in [Tverberg plus constraints, Bull. London Math. Soc. 46:953–967 (2014]). The conditions in this theorem are somewhat weaker than in the original conjecture, and we show that the theorem is optimal in the sense that the new (weakened) condition is also necessary. Among the consequences is a positive answer (Theorem 7.2) to the ‘balanced case’ of the question asking whether each admissible r-tuple is Tverberg prescribable (Blagojevi? et al. 2014, Question 6.9). 相似文献
5.
Wenbin Guo 《Indagationes Mathematicae》2008,19(3):391-399
The existence of a solvable non-normal Fitting class F which is not a Lockett class but for which the Lockett Conjecture still holds are studied. We also prove that there exists an ω-local Fitting class F which does not satisfy the Lockett conjecture but the Lockett conjecture still holds under a given condition. As a consequence of our result, a generalized version of the Lausch's problem in the well-known Kourovka Notebook is answered. 相似文献
6.
Arthur Bartels 《Journal of Pure and Applied Algebra》2006,205(3):660-696
We discuss an analogon to the Farrell-Jones Conjecture for homotopy algebraic K-theory. In particular, we prove that if a group G acts on a tree and all isotropy groups satisfy this conjecture, then G satisfies this conjecture. This result can be used to get rational injectivity results for the assembly map in the Farrell-Jones Conjecture in algebraic K-theory. 相似文献
7.
Teresa W. Haynes Michael A. Henning Lucas C. van der Merwe Anders Yeo 《Central European Journal of Mathematics》2014,12(12):1882-1889
A graph is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Let G be a diameter-2-critical graph of order n. Murty and Simon conjectured that the number of edges in G is at most ?n 2/4? and that the extremal graphs are the complete bipartite graphs K ?n/2?,?n/2?. Fan [Discrete Math. 67 (1987), 235–240] proved the conjecture for n ≤ 24 and for n = 26, while Füredi [J. Graph Theory 16 (1992), 81–98] proved the conjecture for n > n 0 where n 0 is a tower of 2’s of height about 1014. The conjecture has yet to be proven for other values of n. Let Δ denote the maximum degree of G. We prove the following maximum degree theorems for diameter-2-critical graphs. If Δ ≥ 0.7 n, then the Murty-Simon Conjecture is true. If n ≥ 2000 and Δ ≥ 0.6789 n, then the Murty-Simon Conjecture is true. 相似文献
8.
Dmitry N. Kozlov 《Annals of Combinatorics》1997,1(1):67-90
We introduce a new poset property which we call EC-shellability. It is more general than the more established concept of EL-shellability, but it still implies shellability. Because of Theorem 3.10, EC-shellability is entitled to be called general lexicographic shellability. As an application of our new concept, we prove that intersection lattices Πλ of orbit arrangementsA λ are EC-shellable for a very large class of partitions λ. This allows us to compute the topology of the link and the complement for these arrangements. In particular, for this class of λs, we are able to settle a conjecture of Björner [B94, Conjecture 13.3.2], stating that the cohomology groups of the complement of the orbit arrangements are torsion-free. We also present a class of partitions for which Πλ is not shellable, along with other issues scattered throughout the paper. 相似文献
9.
Sarnak's Disjointness Conjecture states that the Möbius function is disjoint with any zeroentropy flow. This note establishes this conjecture, with a rate, for Furstenberg's irregular flows on the infinite-dimensional torus. 相似文献
10.
Disjoint partitions, and its counting, have been widely studied in the literature of optimal partitions and clustering. We give an exact counting on the number of disjoint ordered 2-partitions for n points in general position in R2. We also give an exact counting on the maximum number of disjoint 2-partitions, where one part consists of two points, over all sets of n points in R2. 相似文献
11.
Andrew Suk 《Discrete and Computational Geometry》2013,49(2):280-286
It is shown that every complete $n$ -vertex simple topological graph has at $\varOmega (n^{1/3})$ pairwise disjoint edges, and these edges can be found in polynomial time. This proves a conjecture of Pach and Tóth, which appears as Problem 5 from Chapter 9.5 in Research Problems in Discrete Geometry by Brass, Moser, and Pach. 相似文献
12.
Jaromy Scott Kuhl 《Discrete Mathematics》2008,308(20):4763-4767
The Evans Conjecture states that a partial Latin square of order n with at most n-1 entries can be completed. In this paper we generalize the Evans Conjecture by showing that a partial r-multi Latin square of order n with at most n-1 entries can be completed. Using this generalization, we confirm a case of a conjecture of Häggkvist. 相似文献
13.
《Journal of Pure and Applied Algebra》2023,227(6):107299
We obtain new evidence for the Purely Wild Inertia Conjecture posed by Abhyankar and for its generalization. We show that this generalized conjecture is true for any product of simple Alternating groups in odd characteristics, and for any product of certain Symmetric or Alternating groups in characteristic two. We also obtain important results towards the realization of the inertia groups which can be applied to more general set up. We further show that the Purely Wild Inertia Conjecture is true for any product of perfect quasi p-groups (groups generated by their Sylow p-subgroups) if the conjecture is established for individual groups. 相似文献
14.
Torsten Schöneborn 《Journal of Combinatorial Theory, Series A》2005,112(1):82-104
The Topological Tverberg Theorem claims that any continuous map of a (q-1)(d+1)-simplex to Rd identifies points from q disjoint faces. (This has been proved for affine maps, for d?1, and if q is a prime power, but not yet in general.)The Topological Tverberg Theorem can be restricted to maps of the d-skeleton of the simplex. We further show that it is equivalent to a “Winding Number Conjecture” that concerns only maps of the (d-1)-skeleton of a (q-1)(d+1)-simplex to Rd. “Many Tverberg partitions” arise if and only if there are “many q-winding partitions.”The d=2 case of the Winding Number Conjecture is a problem about drawings of the complete graphs K3q-2 in the plane. We investigate graphs that are minimal with respect to the winding number condition. 相似文献
15.
In this paper, we derive some results giving sufficient conditions for a graph G containing a Hamiltonian path to be Hamiltonian. In particular the Bondy-Chvátal theorem [J. A. Bondy and V. Chvátal, Discrete Math. 15 (1976), 111–135] is derived as a corollary of the main theorem of this paper and hence a more powerful closure operation than the one introduced by Bondy and Chvátal is defined. These results can be viewed as a step towards a unification of the various known results on the existence of Hamiltonian circuits in undirected graphs. Moreover, Theorem 1 of this paper provides a counterpart of the Chvátal-Erdös theorem [V. Chvátal and P. Erdös, Discrete Math. 2 (1972), 111–113] which gives a sufficient condition for a Hamiltonian circuit in terms of global vertex connectivity and independence number. 相似文献
16.
Zassenhaus conjectured that any unit of finite order in the integral group ring of a finite group G is conjugate in the rational group algebra of G to an element in ±G. We review the known weaker versions of this conjecture and introduce a new condition, on the partial augmentations of the powers of a unit of finite order in , which is weaker than the Zassenhaus Conjecture but stronger than its other weaker versions.We prove that this condition is satisfied for units mapping to the identity modulo a nilpotent normal subgroup of G. Moreover, we show that if the condition holds then the HeLP Method adopts a more friendly form and use this to prove the Zassenhaus Conjecture for a special class of groups. 相似文献
17.
Carlos Maquera Jean Venato-Santos 《Bulletin of the Brazilian Mathematical Society》2013,44(2):273-284
Let F: ? n → ? n be a polynomial local diffeomorphism and let S F denote the set of not proper points of F. The Jelonek’s real Jacobian Conjecture states that if codim(S F ) ≥ 2, then F is bijective. We prove a weak version of such conjecture establishing the sufficiency of a necessary condition for the bijectivity of F. 相似文献
18.
Michael Jöllenbeck 《Journal of Pure and Applied Algebra》2006,207(2):261-298
In this paper we study the multigraded Hilbert and Poincaré-Betti series of A=S/a, where S is the ring of polynomials in n indeterminates divided by the monomial ideal a. There is a conjecture about the multigraded Poincaré-Betti series by Charalambous and Reeves which they proved in the case where the Taylor resolution is minimal. We introduce a conjecture about the minimal A-free resolution of the residue class field and show that this conjecture implies the conjecture of Charalambous and Reeves and, in addition, gives a formula for the Hilbert series. Using Algebraic Discrete Morse theory, we prove that the homology of the Koszul complex of A with respect to x1,…,xn is isomorphic to a graded commutative ring of polynomials over certain sets in the Taylor resolution divided by an ideal r of relations. This leads to a proof of our conjecture for some classes of algebras A. We also give an approach for the proof of our conjecture via Algebraic Discrete Morse theory in the general case.The conjecture implies that A is Golod if and only if the product (i.e. the first Massey operation) on the Koszul homology is trivial. Under the assumption of the conjecture we finally prove that a very simple purely combinatorial condition on the minimal monomial generating system of a implies Golodness for A. 相似文献
19.
Benjamin Sambale 《Israel Journal of Mathematics》2018,228(2):513-526
An open conjecture by Harada from 1981 gives an easy characterization of the p-blocks of a finite group in terms of the ordinary character table. Kiyota and Okuyama have shown that the conjecture holds for p-solvable groups. In the present work we extend this result using a criterion on the decomposition matrix. In this way we prove Harada’s Conjecture for several new families of defect groups and for all blocks of sporadic simple groups. In the second part of the paper we present a dual approach to Harada’s Conjecture. 相似文献
20.
We continue our study of partitions of the full set of triples chosen from a v-set into copies of the Fano plane PG(2,2) (Fano partitions) or copies of the affine plane AG(2,3) (affine partitions) or into copies of both of these planes (mixed partitions). The smallest cases for which such partitions can occur are v=8 where Fano partitions exist, v=9 where affine partitions exist, and v=10 where both affine and mixed partitions exist. The Fano partitions for v=8 and the affine partitions for v=9 and 10 have been fully classified, into 11, two and 77 isomorphism classes, respectively. Here we classify (1) the sets of i pairwise disjoint affine planes for i=1,…,7, and (2) the mixed partitions for v=10 into their 22 isomorphism classes. We consider the ways in which these partitions relate to the large sets of AG(2,3). 相似文献