共查询到20条相似文献,搜索用时 906 毫秒
1.
James East 《Semigroup Forum》2010,81(2):357-379
The (full) transformation semigroup Tn\mathcal{T}_{n} is the semigroup of all functions from the finite set {1,…,n} to itself, under the operation of composition. The symmetric group Sn í Tn{\mathcal{S}_{n}\subseteq \mathcal{T}_{n}} is the group of all permutations on {1,…,n} and is the group of units of Tn\mathcal{T}_{n}. The complement Tn\Sn\mathcal{T}_{n}\setminus \mathcal{S}_{n} is a subsemigroup (indeed an ideal) of Tn\mathcal{T}_{n}. In this article we give a presentation, in terms of generators and relations, for Tn\Sn\mathcal{T}_{n}\setminus \mathcal{S}_{n}, the so-called singular part of Tn\mathcal{T}_{n}. 相似文献
2.
The motivation for this paper comes from the Halperin–Carlsson conjecture for (real) moment-angle complexes. We first give
an algebraic combinatorics formula for the M?bius transform of an abstract simplicial complex K on [m]={1,…,m} in terms of the Betti numbers of the Stanley–Reisner face ring k(K) of K over a field k. We then employ a way of compressing K to provide the lower bound on the sum of those Betti numbers using our formula. Next we consider a class of generalized moment-angle
complexes
ZK(\mathbb D, \mathbb S)\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})}, including the moment-angle complex ZK\mathcal{Z}_{K} and the real moment-angle complex
\mathbbRZK\mathbb{R}\mathcal {Z}_{K} as special examples. We show that
H*(ZK(\mathbb D, \mathbb S);k)H^{*}(\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})};\mathbf{k}) has the same graded k-module structure as Tor
k[v](k(K),k). Finally we show that the Halperin–Carlsson conjecture holds for ZK\mathcal{Z}_{K} (resp.
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}) under the restriction of the natural T
m
-action on ZK\mathcal{Z}_{K} (resp. (ℤ2)
m
-action on
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}). 相似文献
3.
We introduce a spanning set of Beilinson–Lusztig–MacPherson type, {A(j, r)}
A,j
, for affine quantum Schur algebras
S\vartriangle(n, r){{{\boldsymbol{\mathcal S}}_\vartriangle}(n, r)} and construct a linearly independent set {A(j)}
A,j
for an associated algebra
[^(K)]\vartriangle(n){{{\boldsymbol{\widehat{\mathcal K}}}_\vartriangle}(n)} . We then establish explicitly some multiplication formulas of simple generators
E\vartriangleh,h+1(0){E^\vartriangle_{h,h+1}}(\mathbf{0}) by an arbitrary element A(j) in
[^(K)]\vartriangle(n){{\boldsymbol{\widehat{{{\mathcal K}}}}_\vartriangle(n)}} via the corresponding formulas in
S\vartriangle(n, r){{{\boldsymbol{\mathcal S}}_\vartriangle(n, r)}} , and compare these formulas with the multiplication formulas between a simple module and an arbitrary module in the Ringel–Hall
algebras
\mathfrak H\vartriangle(n){{{\boldsymbol{\mathfrak H}_\vartriangle(n)}}} associated with cyclic quivers. This allows us to use the triangular relation between monomial and PBW type bases for
\mathfrak H\vartriangle(n){{\boldsymbol{\mathfrak H}}_\vartriangle}(n) established in Deng and Du (Adv Math 191:276–304, 2005) to derive similar triangular relations for
S\vartriangle(n, r){{{\boldsymbol{\mathcal S}}_\vartriangle}(n, r)} and
[^(K)]\vartriangle(n){{\boldsymbol{\widehat{\mathcal K}}}_\vartriangle}(n) . Using these relations, we then show that the subspace
\mathfrak A\vartriangle(n){{{\boldsymbol{\mathfrak A}}_\vartriangle}(n)} of
[^(K)]\vartriangle(n){{\boldsymbol{\widehat{{{\mathcal K}}}}_\vartriangle}(n)} spanned by {A(j)}
A,j
contains the quantum enveloping algebra
U\vartriangle(n){{{\mathbf U}_\vartriangle}(n)} of affine type A as a subalgebra. As an application, we prove that, when this construction is applied to quantum Schur algebras S(n,r){\boldsymbol{\mathcal S}(n,r)} , the resulting subspace
\mathfrak A\vartriangle(n){{{{\boldsymbol{\mathfrak A}}_\vartriangle}(n)}} is in fact a subalgebra which is isomorphic to the quantum enveloping algebra of
\mathfrakgln{\mathfrak{gl}_n} . We conjecture that
\mathfrak A\vartriangle(n){{{{{\boldsymbol{\mathfrak A}}_\vartriangle}(n)}}} is a subalgebra of
[^(K)]\vartriangle(n){{\boldsymbol{\widehat{{{\mathcal K}}}}_\vartriangle}(n)} . 相似文献
4.
Y. C. Wang 《Acta Mathematica Hungarica》2012,135(3):248-269
Let Hk\mathcal{H}_{k} denote the set {n∣2|n,
n\not o 1 (mod p)n\not\equiv 1\ (\mathrm{mod}\ p) ∀ p>2 with p−1|k}. We prove that when
X\frac1120(1-\frac12k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{2k}\right) +\varepsilon}\leqq H\leqq X, almost all integers
n ? \allowbreak Hk ?(X, X+H]n\in\allowbreak {\mathcal{H}_{k} \cap (X, X+H]} can be represented as the sum of a prime and a k-th power of prime for k≧3. Moreover, when
X\frac1120(1-\frac1k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{k}\right) +\varepsilon}\leqq H\leqq X, almost all integers n∈(X,X+H] can be represented as the sum of a prime and a k-th power of integer for k≧3. 相似文献
5.
In this paper we give the conditions on the pair (ω
1, ω
2) which ensures the boundedness of the anisotropic maximal operator and anisotropic singular integral operators from one generalized
Morrey space Mp,w1 \mathcal{M}_{p,\omega _1 } to another Mp,w2 \mathcal{M}_{p,\omega _2 }, 1 < p < g8, and from the space M1,w1 \mathcal{M}_{1,\omega _1 } to the weak space WM1,w2 W\mathcal{M}_{1,\omega _2 }. 相似文献
6.
Martin Kassabov 《Inventiones Mathematicae》2007,170(2):327-354
We construct explicit generating sets S
n
and of the alternating and the symmetric groups, which turn the Cayley graphs and into a family of bounded degree expanders for all n. 相似文献
7.
Stevan Pilipovi? Nenad Teofanov Joachim Toft 《Journal of Fourier Analysis and Applications》2011,17(3):374-407
Let ω,ω
0 be appropriate weight functions and q∈[1,∞]. We introduce the wave-front set, WFFLq(w)(f)\mathrm{WF}_{\mathcal{F}L^{q}_{(\omega)}}(f) of f ? S¢f\in \mathcal{S}' with respect to weighted Fourier Lebesgue space FLq(w)\mathcal{F}L^{q}_{(\omega )}. We prove that usual mapping properties for pseudo-differential operators Op (a) with symbols a in S(w0)r,0S^{(\omega _{0})}_{\rho ,0} hold for such wave-front sets. Especially we prove that
$[b]{lll}\mathrm{WF}_{\mathcal{F}L^q_{(\omega /\omega _0)}}(\operatorname {Op}(a)f)&\subseteq&\mathrm{WF}_{\mathcal{F}L^q_{(\omega )}}(f)\\[6pt]&\subseteq&\mathrm{WF}_{\mathcal{F}L^q_{(\omega/\omega _0)}}(\operatorname {Op}(a)f)\cup \operatorname {Char}(a).$\begin{array}[b]{lll}\mathrm{WF}_{\mathcal{F}L^q_{(\omega /\omega _0)}}(\operatorname {Op}(a)f)&\subseteq&\mathrm{WF}_{\mathcal{F}L^q_{(\omega )}}(f)\\[6pt]&\subseteq&\mathrm{WF}_{\mathcal{F}L^q_{(\omega/\omega _0)}}(\operatorname {Op}(a)f)\cup \operatorname {Char}(a).\end{array} 相似文献
8.
Bernd Fritzsche Bernd Kirstein Conrad M?dler 《Complex Analysis and Operator Theory》2011,5(2):447-511
This paper continues recent investigations started in Dyukarev et al. (Complex anal oper theory 3(4):759–834, 2009) into the
structure of the set Hq,2n 3 {\mathcal{H}_{q,2n}^{\ge}} of all Hankel nonnegative definite sequences, (sj)j=02n{(s_{j})_{j=0}^{2n}}, of complex q × q matrices and its important subclasses Hq,2n 3 ,e{\mathcal{H}_{q,2n}^{\ge,{\rm e}}} and ${\mathcal{H}_{q,2n}^>}${\mathcal{H}_{q,2n}^>} of all Hankel nonnegative definite extendable sequences and of all Hankel positive definite sequences, respectively. These
classes of sequences arise quite naturally in the framework of matrix versions of the truncated Hamburger moment problem.
In Dyukarev et al. (Complex anal oper theory 3(4):759–834, 2009) a canonical Hankel parametrization [(Ck)k=1n, (Dk)k=0n]{[(C_k)_{k=1}^n, (D_k)_{k=0}^n]} consisting of two sequences of complex q × q matrices was associated with an arbitrary sequence (sj)j=02n{(s_{j})_{j=0}^{2n}} of complex q × q matrices. The sequences belonging to each of the classes Hq,2n 3 , Hq,2n 3 ,e{\mathcal{H}_{q,2n}^{\ge}, \mathcal{H}_{q,2n}^{\ge,{\rm e}}}, and ${\mathcal{H}_{q,2n}^>}${\mathcal{H}_{q,2n}^>} were characterized in terms of their canonical Hankel parametrization (see, Dyukarev et al. in Complex anal oper theory 3(4):759–834,
2009; Proposition 2.30). In this paper, we will study further aspects of the canonical Hankel parametrization. Using the canonical
Hankel parametrization [(Ck)k=1n, (Dk)k=0n]{[(C_k)_{k=1}^n, (D_k)_{k=0}^n]} of a sequence (sj)j=02n ? Hq,2n 3 {(s_{j})_{j=0}^{2n} \in \mathcal{H}_{q,2n}^{\ge}}, we give a recursive construction of a monic right (resp. left) orthogonal system of matrix polynomials with respect to (sj)j=02n{(s_{j})_{j=0}^{2n}} (see Theorem 5.5). The matrices [(Ck)k=1n, (Dk)k=0n]{[(C_k)_{k=1}^n, (D_k)_{k=0}^n]} will be expressed in terms of an arbitrary monic right (resp. left) orthogonal system with respect to (sj)j=02n{(s_{j})_{j=0}^{2n}} (see Theorem 5.11). This result will be reformulated in terms of nonnegative Hermitian Borel measures on
\mathbbR{\mathbb{R}}. In this way, integral representations for the matrices [(Ck)k=1n, (Dk)k=0n]{[(C_k)_{k=1}^n, (D_k)_{k=0}^n]} will be obtained (see Theorem 6.9). Starting from the monic orthogonal polynomials with respect to some classical probability
distributions on
\mathbbR{\mathbb{R}}, Theorem 6.9 is used to compute the canonical Hankel parametrization of their moment sequences. Moreover, we discuss important
number sequences from enumerative combinatorics using the canonical Hankel parametrization. 相似文献
9.
A. Krajka 《Acta Appl Math》2007,96(1-3):327-338
Let
be a probability space with a nonatomic measure P and let (S,ρ) be a separable complete metric space. Let {N
n
,n≥1} be an arbitrary sequence of positive-integer valued random variables. Let {F
k
,k≥1} be a family of probability laws and let X be some random element defined on
and taking values in (S,ρ).
In this paper we present necessary and sufficient conditions under which one can construct an array of random elements {X
n,k
,n,k≥1} defined on the same probability space and taking values in (S,ρ), and such that
, and moreover
as n→∞. Furthermore, we consider the speed of convergence
to X as n→∞.
相似文献
10.
Fix any n≥1. Let X
1,…,X
n
be independent random variables such that S
n
=X
1+⋅⋅⋅+X
n
, and let
S*n=sup1 £ k £ nSkS^{*}_{n}=\sup_{1\le k\le n}S_{k}
. We construct upper and lower bounds for s
y
and
sy*s_{y}^{*}
, the upper
\frac1y\frac{1}{y}
th quantiles of S
n
and
S*nS^{*}_{n}
, respectively. Our approximations rely on a computable quantity Q
y
and an explicit universal constant γ
y
, the latter depending only on y, for which we prove that
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