Báo cáo toán học: "Regular character tables of symmetric groups" docx

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Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 09:46

... E. R. van Dam and W. H. Haemers, Eigenvalues and the diameter of graphs, Linear and Multilinear Algebra 39 (1995), 33–44. [8] E. R. van Dam and W. H. Haemers, A characterization of distance-regular ... study two spectral characterizations of antipodal distance-regular graphs. The fist one establishes that the distance-regular graphs which are antipodal the electronic journal...

Ngày tải lên: 07/08/2014, 06:22

... n)k −1 φ(k). In either case, the inequality in part 1 of the lemma holds. On the number of perfect matchings and Hamilton cycles in -regular non-bipartite graphs Alan Frieze ∗ Department of Mathematical ... of combinatorics 7 (2000), #R57 4 3 Hamilton Cycles A Hamilton cycle is the union of two perfect matchings and so h(G) ≤ 1 2 m(G) 2 a...

Ngày tải lên: 07/08/2014, 06:22

... orbits of Singer groups or subgroups of Singer groups. It seems, however, that only point (and, in the case the electronic journal of combinatorics 9 (2002), #R15 8 orbits of any Singer cycle of Σ n−1 on ... In the statement of the following theorem, à denotes the Măobius function, the basic properties of which can be found in, for example, [1]. Theore...

Ngày tải lên: 07/08/2014, 06:23

... determinant of the character tables of finite symmetric groups. It is a well-known fact that if X n is the character table of the symmetric group S n , then the absolute value of the determinant of X n equals ... as the product of all parts of all partitions of n. It also equals b n , which is defined as the product of all factorials of all multiplicities of part...

Ngày tải lên: 07/08/2014, 07:21

... |Γ|≤m! and the subset {y 1 , ,y j } satisfies 1. φ(y i )=i for each i, 2. y i+1 is in Γ i−1 .y i for each i from 2 to j − 1, and y 1 is in Γ j−1 .y j , then j ≤ m and |Γ i−1 .y i |≥j − i + 2for each ... shows this and two other graphs with the same automorphism group and demonstrates that all three have different distinguishing numbers. This example disproves a conjecture in [...

Ngày tải lên: 07/08/2014, 08:20

... recoverable using any algorithm designed to compute the product of an adjacency matrix of the graph and an arbitrary vector. The linear complexity of a graph may therefore be seen as a measure of ... adjacency matrices of graphs, and a working knowledge of the linear complexity of a linear transformation. An excellent reference for linear complexity, and al...

Ngày tải lên: 07/08/2014, 13:21

... runs over all equivalence classes of prime, reduced cycles of G, and | C | is the length of C. Zeta functions of graphs started from zeta functions of regular graphs by Ihara [8]. In [8], he showed ... Sato [10] showed that the zeta function of a regular covering of G is a product of L -functions of G. Stark and Terras [16] treated zeta functions of bipartit...

Ngày tải lên: 07/08/2014, 13:21

... and y. Then G is a 4 -regular graph, and G has a 1-factor con- taining e and a 1-factor avoiding e. According to Theorem 3, G has a k-factor containing e and a k-factor avoiding e for every k ... containing e and a 1-factor avoiding e, then G has a k-factor containing e and a k-factor avoiding e for every k ∈ {1, 2, . . . , r − 1}. Proof. Let F and F e be two...

Ngày tải lên: 07/08/2014, 13:21

... regular graph and e be an edge of G. If H is a component of G e with à (H) = à (G e) , then à (G) µ (H) > 1 Diam (H) |H| . This lemma follows easily from Theorem 2.1 of [2] and its proof ... its proof is omitted. Proofs Proof of Theorem 2 Write dist F (s, t) for the length of a shortest path joining two vertices s and t in a graph F. Write d for the degree of G, let H = G uv,...

Ngày tải lên: 07/08/2014, 13:21

... referee for the useful remarks. the electronic journal of combinatorics 14 (2007), #N21 6 Regular spanning subgraphs of bipartite graphs of high minimum degree B´ela Csaba ∗† Submitted: Aug 1, 2007; ... electronic journal of combinatorics 14 (2007), #N21 2 3.2 Proof of part II For proving part II of the theorem we want to construct a class of balanced bipartite...

Ngày tải lên: 07/08/2014, 15:22

... get the numerator of the right-hand side of (4.10). Divide this number of choices by the number of permutations of {1, . . . , rn} to deduce the lemma. ✷ Using the methods in the proof of Theorem ... := r i=1 A i . Let m ∈ min(p, q). Then perm m A is the number of m -matchings of G := ∨ r i=1 G i , which is equal to the number of m -matchings o...

Ngày tải lên: 07/08/2014, 21:20

... characterization of completely pseudo-regular codes in algebraic sense, which coincides with the one of Theorem 3.3. This proves the equivalence between combinatorial and algebraic approaches to completely pseudo-regular ... So, once proved, we speak indistinctly of one or another concept. Theorem 4.2 A se t of v ertices C ⊂ V of a graph Γ is a completely pseudo-regul...

Ngày tải lên: 08/08/2014, 12:22

... root of f 1 (x) = 0. This completes the proof. ✷ 3 The proof of The orems 1.5 and 1.6 We will need the following technical lemma whose proof is an easy modification of the proof of Theorem 2.2 from ... graph G of order v has a 1-factor when v is even, and a matching of order v − 1 when v is odd. In [11], the author studied the relation of eigenvalues and regular factors of...

Ngày tải lên: 08/08/2014, 12:23