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A combinatorial proof of Klyachko’s Theorem on Lie representations
Springer Science and Business Media LLC - Tập 23 - Trang 225-230 - 2006
L. G. Kovács, Ralph Stöhr
Let L be a free Lie algebra of finite rank r over an arbitrary field K of characteristic 0, and let L n denote the homogeneous component of degree n in L. Viewed as a module for the general linear group GL(r,K), L n is known to be semisimple with the isomorphism types of the simple summands indexed by partitions of n with at most r parts. Klyachko proved in 1974 that, for n > 6, almost all such pa... hiện toàn bộ
A family of edge-transitive Cayley graphs
Springer Science and Business Media LLC - Tập 49 Số 2 - Trang 147-167 - 2019
Jiangmin Pan, Zhaofei Peng
Unimodular Triangulations and Coverings of Configurations Arising from Root Systems
Springer Science and Business Media LLC - Tập 14 - Trang 199-219 - 2001
Hidefumi Ohsugi, Takayuki Hibi
Existence of a regular unimodular triangulation of the configuration $$\Phi ^ + \cup \{ (0,0,...,0)\} {\text{ in }}R^n$$ , where Φ+ is the collection of the positive roots of a root system $$\Phi \subset R^n $$ and where (0, 0,...,0 ) is the origin of $$R^n $$ , will be shown for Φ = B n , C n , D n and BC n . Moreover, existence of a unimodular covering of a certain subconfiguration of the config... hiện toàn bộ
Residues formulas for the push-forward in K-theory, the case of $$\mathbf{G}_2/P$$
Springer Science and Business Media LLC - Tập 49 - Trang 361-380 - 2018
Andrzej Weber, Magdalena Zielenkiewicz
We study residue formulas for push-forward in the equivariant K-theory of homogeneous spaces. For the classical Grassmannian, the residue formula can be obtained from the cohomological formula by a substitution. We also give another proof using symplectic reduction and the method involving the localization theorem of Jeffrey–Kirwan. We review formulas for other classical groups, and we derive them... hiện toàn bộ
The Irreducible Modules of the Terwilliger Algebras of Doob Schemes
Springer Science and Business Media LLC - Tập 6 - Trang 173-195 - 1997
Kenichiro Tanabe
Let Y be any commutative association scheme and we fix any vertex x of Y. Terwilleger introduced a non-commutative, associative, and semi-simple C-algebraT=T(x) for Y and x in [4]. We call T the Terwilliger (or subconstituent) algebra ofY with respect to x. Let $$W( \subset C^{|X|} ) $$ be an irreducible T(x)-module. W is said to be thin if W satisfies a certain simple condition.Y is said to be th... hiện toàn bộ
On automorphism groups of quasiprimitive 2-arc transitive graphs
Springer Science and Business Media LLC - Tập 28 - Trang 261-270 - 2007
Cai Heng Li
We characterize the automorphism groups of quasiprimitive 2-arc-transitive graphs of twisted wreath product type. This is a partial solution for a problem of Praeger regarding quasiprimitive 2-arc transitive graphs. The solution stimulates several further research problems regarding automorphism groups of edge-transitive Cayley graphs and digraphs.
On computing Schur functions and series thereof
Springer Science and Business Media LLC - Tập 50 - Trang 127-141 - 2018
Cy Chan, Vesselin Drensky, Alan Edelman, Raymond Kan, Plamen Koev
In this paper, we present two new algorithms for computing all Schur functions $$s_\kappa (x_1,\ldots ,x_n)$$ for partitions $$\kappa $$ such that $$|\kappa |\le N$$ . For nonnegative arguments, $$x_1,\ldots ,x_n$$ , both algorithms are subtraction-free and thus each Schur function is computed to high relative accuracy in floating point arithmetic. The cost of each algorithm per Schur function is ... hiện toàn bộ
Các đồ thị Cayley tứ phân cạnh chuyển vị của các nhóm Frobenius Dịch bởi AI
Springer Science and Business Media LLC - Tập 53 - Trang 527-551 - 2021
Lei Wang, Yin Liu, Yanxiong Yan
Trong bài báo này, chúng tôi đưa ra một đặc điểm cho một lớp đồ thị Cayley chuyển vị theo cạnh và cung cấp một phương pháp để xây dựng các đồ thị chuyển vị theo cạnh với bậc 4 có ổ đĩa đỉnh lớn một cách tùy ý. Đặc biệt, trong phần cuối, chúng tôi thu được một số mở rộng của các kết quả của Li và cộng sự (Các đồ thị Cayley tứ phân cạnh chuyển vị với số đỉnh lẻ, Tạp chí Suy diễn Tổ hợp Seri B 96:164... hiện toàn bộ
#đồ thị Cayley #tứ phân cạnh #chuyển vị #nhóm Frobenius #ổ đĩa đỉnh
Factorization patterns on nonlinear families of univariate polynomials over a finite field
Springer Science and Business Media LLC - Tập 51 - Trang 103-153 - 2019
Guillermo Matera, Mariana Pérez, Melina Privitelli
We estimate the number $$|\mathcal {A}_{{\varvec{\lambda }}}|$$ of elements on a nonlinear family $$\mathcal {A}$$ of monic polynomials of $$\mathbb {F}_{q}[T]$$ of degree r having factorization pattern $${\varvec{\lambda }}:=1^{\lambda _1}2^{\lambda _2}\ldots r^{\lambda _r}$$. We show that $$|\mathcal {A}_{{\varvec{\lambda }}}|= \mathcal {T}({\varvec{\lambda }})\,q^{r-m}+\mathcal {O}(q^{r-m-{1}/{... hiện toàn bộ
A complete classification of 5-regular circulant graphs that allow cyclic orthogonal double covers
Springer Science and Business Media LLC - Tập 53 - Trang 593-611 - 2021
M. Higazy, R. Scapellato, Y. S. Hamed
Graph theory and its applications attract several researchers from different areas of research. It is used to model wide range of systems, for example in biological system and in studying chaotic systems. Decomposition of complex graphs into simple small graphs is very helpful to study that complex systems. A complete classification is given for circulant graphs of degree 5 that allow an Orthogona... hiện toàn bộ
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