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61.
《Discrete Mathematics》2019,342(9):2570-2578
Chen proposed a conjecture on the log-concavity of the generating function for the symmetric group with respect to the length of longest increasing subsequences of permutations. Motivated by Chen’s log-concavity conjecture, Bóna, Lackner and Sagan further studied similar problems by restricting the whole symmetric group to certain of its subsets. They obtained the log-concavity of the corresponding generating functions for these subsets by using the hook-length formula. In this paper, we generalize and prove their results by establishing the Schur positivity of certain symmetric functions. This also enables us to propose a new approach to Chen’s original conjecture. 相似文献
62.
《Discrete Mathematics》2021,344(12):112598
We study the Ihara zeta function of the complement of a semiregular bipartite graph. A factorization formula for the Ihara zeta function is derived via which the number of spanning trees is computed. For a class of complements of semiregular bipartite graphs, it is shown that they have the same Ihara zeta function if and only if they are cospectral. 相似文献
63.
Let (l) and n be positive integers such that l ≥ n,and let Gn,l be the Grassmannian which consists of the set of n-dimensional subspaces of Cl.There is a Z-graded algebra isomorphism between the cohomology H*(Gn,l,Z) of Gn,l and a nat-ural Z-form B of the Z-graded basic algebra of the type A cyclotomic nilHecke algebra(H)(0) =<ψ1,… ψn-1,y1,…,yn>.We show that the isomorphism can be chosen such that the image of each (geometrically defined) Schubert class (a1,...,an) coincides with the basis element bλ constructed by Hu and Liang by purely algebraic method,where 0 ≤ a1 ≤ a2 ≤ … ≤ an ≤ l-n with ai ∈ Z for each i,and λ is the l-multipartition of n associated to (l + 1-(an + n),l + 1-(an-1 + n-1),...,l + 1-(a1 + 1)).A similar correspondence between the Schubert class basis of the cohomology of the Grassmanni-an Gl-n,l and the bλ's basis (λ is an l-multipartition of n with each component being either (1) or empty) of the natural Z-form B of the Z-graded basic algebra of (H)(0)l,n is also obtained.As an application,we obtain a second version of the Giambelli formula for Schubert classes. 相似文献
64.
65.
基于溶胶-凝胶技术可更新的安培分析免疫传感器用于人血清中补体3的测定 总被引:2,自引:0,他引:2
在低温下,通过混合石墨粉,补体3抗血清,溶胶-凝胶而制备了一种基于啼-凝胶技术的可更新的安培分析免疫传感器。该传感器坚固,多孔,拥有一个更新的表面,在辣根过氧化物酶标记的补体3的协助下,通过竞争性的免疫分析来确定人血清中补体3的含量。以邻-氨酚作为底物,-150mV作为工作电位,响应电流与补体3的浓度在1.17-35.1μg/mL范围内呈线性关系,检出限为0.56μg/mL。分析血清样本结果表明所制备的传感器在临床分析中是可行的。 相似文献
66.
Let S f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S f , a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms. 相似文献
67.
Let A be a complex n × n matrix, and let A = B + iC, B = B*, C = C* be its Toeplitz decomposition. Then A is said to be (strictly) accretive if B > 0 and (strictly) dissipative if C > 0. We study the properties of matrices that satisfy both these conditions, in other words, of accretive-dissipative matrices. In many respects, these matrices behave as numbers in the first quadrant of the complex plane. Some other properties are natural extensions of the corresponding properties of Hermitian positive-definite matrices.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 832–843.Original Russian Text Copyright ©2005 by A. George, Kh. D. Ikramov. 相似文献
68.
Bin Zhu 《Journal of Algebraic Combinatorics》2008,27(1):35-54
We give a quiver representation theoretic interpretation of generalized cluster complexes defined by Fomin and Reading. Using
d-cluster categories defined by Keller as triangulated orbit categories of (bounded) derived categories of representations
of valued quivers, we define a d-compatibility degree (−∥−) on any pair of “colored” almost positive real Schur roots which generalizes previous definitions on the noncolored case
and call two such roots compatible, provided that their d-compatibility degree is zero. Associated to the root system Φ corresponding to the valued quiver, using this compatibility relation, we define a simplicial complex which has colored almost
positive real Schur roots as vertices and d-compatible subsets as simplices. If the valued quiver is an alternating quiver of a Dynkin diagram, then this complex is
the generalized cluster complex defined by Fomin and Reading.
Supported by the NSF of China (Grants 10471071) and by the Leverhulme Trust through the network ‘Algebras, Representations
and Applications’. 相似文献
69.
70.
Schur不等式的改进与特征值的估计 总被引:2,自引:0,他引:2
设复矩阵A的特征值为λ1,…,λn.本文的目的,首先给出和的不等式用以改进Schur不等式,然后应用这些不等式去估计矩阵A的特征值. 相似文献