共查询到20条相似文献,搜索用时 15 毫秒
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§1. IntroductionByaBCI-algebrawemeananalgebra(X,,0)oftype(2,0)withthefollowingcondi-tions:(1)((xy)(xz))(zy)=0;(2)(x(xy))y=0;(3)xx=0;(4)xy=yx=0impliesx=y.IfaBCI-algebra(X,,0)satisfies(5)0x=0.thenitiscalledaBCK-algebra.InaBCI-algebra,thef… 相似文献
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The spectrum of path factorization of bipartite multigraphs 总被引:1,自引:0,他引:1
Jian WANG~ Bei-liang DU~ 《中国科学A辑(英文版)》2007,50(7):1045-1054
LetλK_(m,n)be a bipartite multigraph with two partite sets having m and n vertices, respectively.A P_v-factorization ofλK_(m,n)is a set of edge-disjoint P_v-factors ofλK_(m,n)which partition the set of edges ofλK_(m,n).When v is an even number,Ushio,Wang and the second author of the paper gave a necessary and sufficient condition for the existence of a P_v-factorization ofλK_(m,n).When v is an odd number,we have proposed a conjecture.Very recently,we have proved that the conjecture is true when v=4k-1.In this paper we shall show that the conjecture is true when v = 4k 1,and then the conjecture is true.That is,we will prove that the necessary and sufficient conditions for the existence of a P_(4k 1)-factorization ofλK_(m,n)are(1)2km≤(2k 1)n,(2)2kn≤(2k 1)m,(3)m n≡0(mod 4k 1),(4)λ(4k 1)mn/[4k(m n)]is an integer. 相似文献
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By means of partial fraction decomposition, we give simple proofs of Mortenson’s identities first. Then, inspired by them, we derive their q-generalizations and explore further identities of similar type. 相似文献
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We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) cyclotomic Khovanov-Lauda
algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki’s categorification
theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial ℤ-grading on blocks of
cyclotomic Hecke algebras, including symmetric groups in positive characteristic. 相似文献
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Ehsan Tavanfar 《Archiv der Mathematik》2017,109(5):429-439
In this article, applying the quasi-Gorenstein analogous of the Ulrich’s deformation of certain Gorenstein rings to unique factorization domains, we show that the Small Cohen–Macaulay Conjecture reduces to excellent unique factorization domains. 相似文献
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Generalizing the work of Farahat-Higman on symmetric groups, we describe the structures of the even centers
of integral spin symmetric group superalgebras, which lead to universal algebras termed as the spin FH-algebras. A connection
between the odd Jucys-Murphy elements and the Catalan numbers is developed and then used to determine the algebra generators
of the spin FH-algebras and of the even centers
. 相似文献
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Allan Berele 《代数通讯》2013,41(1-2):139-147
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Let σ be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t;σ]∕fK[t;σ] obtained when the twisted polynomial f∈K[t;σ] is invariant, and were first defined by Petit. We compute all their automorphisms if σ commutes with all automorphisms in AutF(K) and n≥m?1, where n is the order of σ and m the degree of f, and obtain partial results for n<m?1. In the case where K∕F is a finite Galois field extension, we obtain more detailed information on the structure of the automorphism groups of these nonassociative unital algebras over F. We also briefly investigate when two such algebras are isomorphic. 相似文献
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Andrzej Walendziak 《Algebra Universalis》1993,30(3):319-330
We introduce the concept of a -representation of an algebraA which is a common generalization of direct and subdirect representation ofA. Here we characterize irredundant -representations in terms of congruence relations. The main result of this paper asserts some uniqueness in such representations.Presented by A. F. Pixley. 相似文献
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Jason P. Bell 《Journal of Number Theory》2006,117(1):160-190
This paper shows that the natural setting for the Bateman and Erd?s study of monotonicity of the kth difference of partition functions a(n) is the class of partition identities
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Richard J. McIntosh 《The Ramanujan Journal》2018,45(3):767-779
In their paper “A survey of classical mock theta functions”, Gordon and McIntosh observed that the classical mock \(\theta \)-functions, including those found by Ramanujan, can be expressed in terms of two ‘universal’ mock \(\theta \)-functions denoted by \(g_{_{2}}\) and \(g_{_{3}}\). These functions are normalized level 2 and level 3 Appell–Lerch functions. In the survey paper, the authors list several identities for certain Appell–Lerch functions and refer the proofs to a future paper with this title, listed in their references as [GM3]. The purpose of this paper is to prove these identities. One of the identities removes the \( \theta \) -quotients from Kang’s formulas, which express \(g_{_{2}}\) and \({g}_{{_{3}}}\) in terms of Zwegers’ \(\mu \)-function and \( \theta \)-quotients. 相似文献
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We augment Restorff's classification of purely infinite Cuntz–Krieger algebras by describing the range of his invariant on purely infinite Cuntz–Krieger algebras. We also describe its range on purely infinite graph C?-algebras with finitely many ideals, and provide ‘unital’ range results for purely infinite Cuntz–Krieger algebras and unital purely infinite graph C?-algebras. 相似文献
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Mathematische Zeitschrift - We categorify various finite-type cluster algebras with coefficients using completed orbit categories associated to Frobenius categories. Namely, the Frobenius... 相似文献
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Leonid Bedratyuk 《Linear and Multilinear Algebra》2013,61(6):789-803
Let ? d 1, d 2 and 𝒞 d 1, d 2 be the algebras of simultaneous invariants and simultaneous covariants of the two binary forms of degrees d 1 and d 2. Formulas for computation of the Poincaré series 𝒫? d 1, d 2 (z), 𝒫𝒞 d 1, d 2 (z) of the algebras are found. By using these formulas, we have computed the series for d 1, d 2 ≤ 20. 相似文献
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Tim Stokes 《Semigroup Forum》2010,81(2):325-334
We characterize algebras of transformations on a set under the operations of composition and the pointwise switching function defined as follows: (f,g)[h,k](x)=h(x) if f(x)=g(x), and k(x) otherwise. The resulting algebras are both semigroups and comparison algebras in the sense of Kennison. The same characterization holds for partial transformations under composition and a suitable generalisation of the quaternary operation in which agreement of f,g includes cases where neither is defined. When a zero element is added (modelling the empty function), the resulting signature is rich enough to encompass many operations on semigroups of partial transformations previously considered, including set difference and intersection, restrictive product, and a functional analog of union. When an identity element is also added (modelling the identity function), further domain-related operations can be captured. 相似文献
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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
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G. A. Akishev 《Russian Mathematics (Iz VUZ)》2009,53(2):21-29
In this paper we estimate the order of approximation of S. M. Nikol’skii and O. V. Besov classes in the norm of the anisotropic Lorentz space. We also obtain bounds for ortho-diameters of these classes. 相似文献