共查询到20条相似文献,搜索用时 15 毫秒
1.
Bodan Arsovski 《Israel Journal of Mathematics》2011,182(1):505-508
We prove Snevily’s conjecture, which states that for any positive integer k and any two k-element subsets {a
1, …, a
k
} and {b
1, …, b
k
} of a finite abelian group of odd order there exists a permutation π ∈ S
k
such that all sums a
i
+ b
π(i) (i ∈ [1, k]) are pairwise distinct. 相似文献
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A proof of Sethares'''' conjecture 总被引:1,自引:0,他引:1
YAO GuowuSchool of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2004,47(2):236-244
Let (?)(z) be holomorphic in the unit disk △ and meromorphic on △. Suppose / is a Teichmuller mapping with complex dilatation In 1968, Sethares conjectured that f is extremal if and only if either (i)(?) has a double pole or (ii)(?) has no pole of order exceeding two on (?)△. The "if" part of the conjecture had been solved by himself. We will give the affirmative answer to the "only if" part of the conjecture. In addition, a more general criterion for extremality of quasiconformal mappings is constructed in this paper, which generalizes the "if" part of Sethares' conjecture and improves the result by Reich and Shapiro in 1990. 相似文献
5.
An assignment problem is the optimization problem of finding, in an m by n matrix of nonnegative real numbers, k entries, no two in the same row or column, such that their sum is minimal. Such an optimization problem is called a random assignment problem if the matrix entries are random variables. We give a formula for the expected value of the optimal k-assignment in a matrix where some of the entries are zero, and all other entries are independent exponentially distributed random variables with mean 1. Thereby we prove the formula 1+1/4+1/9+...+1/k
2
conjectured by G. Parisi for the case k=m=n, and the generalized conjecture of D. Coppersmith and G. B. Sorkin for arbitrary k, m and n.
AcknowledgementWe thank Mireille Bousquet-Mélou and Gilles Schaeffer for introducing the problem to us. We also thank an anonymous referee for suggesting some improvements of the exposition. 相似文献
6.
Daniel Daners 《Archiv der Mathematik》2011,96(2):187-199
The paper is a discussion of Krahn’s proof of the Rayleigh conjecture that amongst all membranes of the same area and the
same physical properties, the circular one has the lowest ground frequency. We show how his approach coincides with the modern
techniques of geometric measure theory using the co-area formula. We furthermore discuss some issues and generalisations of
his proof. 相似文献
7.
For a lattice L, let Princ(L) denote the ordered set of principal congruences of L. In a pioneering paper, G. Grätzer characterized the ordered set Princ(L) of a finite lattice L; here we do the same for a countable lattice. He also showed that every bounded ordered set H is isomorphic to Princ(L) of a bounded lattice L. We prove a related statement: if an ordered set H with a least element is the union of a chain of principal ideals (equivalently, if 0 \({\in}\) H and H has a cofinal chain), then H is isomorphic to Princ(L) of some lattice L. 相似文献
8.
Péter Komjáth 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2017,87(2):337-341
We consider the infinite form of Hadwiger’s conjecture. We give a(n apparently novel) proof of Halin’s 1967 theorem stating that every graph X with coloring number \(>\kappa \) (specifically with chromatic number \(>\kappa \)) contains a subdivision of \(K_\kappa \). We also prove that there is a graph of cardinality \(2^\kappa \) and chromatic number \(\kappa ^+\) which does not contain \(K_{\kappa ^+}\) as a minor. Further, it is consistent that every graph of size and chromatic number \(\aleph _1\) contains a subdivision of \(K_{\aleph _1}\). 相似文献
9.
János Barát 《Discrete Mathematics》2019,342(5):1520-1527
Thomassen formulated the following conjecture: Every 3-connected cubic graph has a red–blue vertex coloring such that the blue subgraph has maximum degree 1 (that is, it consists of a matching and some isolated vertices) and the red subgraph has minimum degree at least 1 and contains no 3-edge path. We prove the conjecture for Generalized Petersen graphs.We indicate that a coloring with the same properties might exist for any subcubic graph. We confirm this statement for all subcubic trees. 相似文献
10.
We give a new proof of Faber?s intersection number conjecture concerning the top intersections in the tautological ring of the moduli space of curves Mg. The proof is based on a very straightforward geometric and combinatorial computation with double ramification cycles. 相似文献
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Akira Kamibeppu 《Discrete Mathematics》2012,312(6):1123-1127
A hole of a graph is an induced cycle of length at least 4. Kim (2005) [3] conjectured that the competition number is bounded by for any graph , where is the number of holes of . Li and Chang (2009) [5] proved that the conjecture is true for a graph whose holes all satisfy a property called ‘independence’. In this paper, by using similar proof techniques in Li and Chang (2009) [5], we prove the conjecture for graphs satisfying two conditions that allow the holes to overlap a lot. 相似文献
13.
Hossein Hajiabolhassan 《Discrete Mathematics》2011,311(23-24):2663-2668
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The pebbling number of a graph G, f(G), is the least n such that, no matter how n pebbles are placed on the vertices of G,
we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on
an adjacent vertex. Graham conjectured that for any connected graphs G and H, f( G x H) ⩽ f( G) f( H). We show that Graham’s
conjecture holds true of a complete bipartite graph by a graph with the two-pebbling property. As a corollary, Graham’s conjecture
holds when G and H are complete bipartite graphs. 相似文献
16.
DU Beiliang & WANG Jian Department of Mathematics Suzhou University Suzhou China Nantong Vocational College Nantong China 《中国科学A辑(英文版)》2006,49(3)
Let Km,n be a complete bipartite graph with two partite sets having m and n vertices, respectively. A Pv-factorization of Km,n is a set of edge-disjoint Pv-factors of Km,n which partition the set of edges of Km,n. When v is an even number, Wang and Ushio gave a necessary and sufficient condition for existence of Pv-factorization of Km,n. When k is an odd number, Ushio in 1993 proposed a conjecture. Very recently, we have proved that Ushio's conjecture is true when v = 4k-1. In this paper we shall show that Ushio Conjecture is true when v = 4k 1, and then Ushio's conjecture is true. That is, we will prove that a necessary and sufficient condition for the existence of a P4k 1-factorization of Km,n is (i) 2km≤ (2k 1)n, (ii) 2kn≤ (2k 1)m, (iii) m n = 0 (mod 4k 1), (iv) (4k 1)mn/[4k(m n)] is an integer. 相似文献
17.
Andrew Berget 《Linear algebra and its applications》2009,430(2-3):791-794
18.
A short proof of V.A. Stetsenko’s theorem on weakly read-many Boolean functions is given, which is based on the technique of representing read-once functions in the form of trees. 相似文献
19.
We generalize the ??motivated proof?? of the Rogers?CRamanujan identities given by Andrews and Baxter to provide an analogous ??motivated proof?? of Gordon??s generalization of the Rogers?CRamanujan identities. Our main purpose is to provide insight into certain vertex-algebraic structure being developed. 相似文献
20.
Sirous Moradi 《Annali dell'Universita di Ferrara》2012,58(1):119-125
In this paper we provide a simple proof of the existence coupled fixed point theorem in complete cone metric spaces due to Sabetghadam et al. (Fixed Point Theory Appl 2009:8, 2009) and due to Olatinwo (Annali Dell’Universita’Di Ferrara 57:173–180, 2011). In particular we prove that these results are spacial cases of Rezapour and Hamlbarani’s theorems (J Math Anal Appl 345(2):719–724, 2008). 相似文献