Several modules M over algebras with straightening law A have a structure which is similar to the structure of A itself: M has a system of generators endowed with a natural partial order, a standard basis over the ring B of coefficients, and the multiplication A × M → A satisfies a “straightening law”. We call them modules with straightening law, briefly MSLs. In section 1 we recall the notion ...

We prove a certain Riemann-Roch type formula for symmetric powers of Galois modules on Dedekind schemes which, in the number field or function field case, specializes to a formula of Burns and Chinburg for Cassou-Noguès-Taylor operations. Introduction Let G be a finite group and E a number field. Let OE denote the ring of integers in E, Y := Spec(OE), and Cl(OYG) := ker(rank : K0(OEG) → Z) the ...

With the advent and development of the Internet of Things, new needs arose and more attention was paid to these needs. These needs include: low power consumption, low area consumption, low supply voltage, higher security and so on. Many solutions have been proposed to improve each one of these needs. In this paper, we try to reduce the power consumption and enhance the security by using SPGAL, ...

We give a representation of the classical theory of multiplicative arithmetic functions (MF)in the ring of symmetric polynomials. The basis of the ring of symmetric polynomials that we use is the isobaric basis, a basis especially sensitive to the combinatorics of partitions of the integers. The representing elements are recursive sequences of Schur polynomials evaluated at subrings of the comp...

A new algorithm for the computation of the spectral expansion of the eigenvalues and eigenvectors of a random non-symmetric matrix is proposed. The algorithm extends the deterministic inverse power method using a spectral discretization approach. The convergence and accuracy of the algorithm is studied for both symmetric and non-symmetric matrices. The method turns out to be efficient and robus...

Purpose. To evaluate surgically induced astigmatism (SIA) and the average corneal power change in symmetric intrastromal corneal ring segment (ICRS) implantation. Methods. The study included 34 eyes of 34 keratoconus patients who underwent symmetric Intacs SK ICRS implantation. The corneal pocket incision meridian was the preoperative steep meridian. Corneal power data were obtained before and ...

The chromatic quasisymmetric function of a graph was introduced by Shareshian and Wachs as a refinement of Stanley’s chromatic symmetric function. An explicit combinatorial formula, conjectured by Shareshian and Wachs, expressing the chromatic quasisymmetric function of the incomparability graph of a natural unit interval order in terms of power sum symmetric functions, is proven. The proof use...

LetM be a tensor category with coefficients in a fieldK of characteristic 0, that is, a K-linear pseudo-abelian symmetric monoidal category such that the tensor product ⊗ of M is bilinear. Then symmetric and exterior powers of an object M ∈ M make sense, by using appropriate projectors relative to the action of the symmetric groups on tensor powers of M . One may therefore introduce the zeta fu...

We develop a general approach to the study of maximal nilpotent subsemigroups of finite semigroups. This approach can be used to recover many known classifications of maximal nilpotent subsemigroups, in particular, for the symmetric inverse semigroup, the symmetric semigroup, and the factor power of the symmetric group. We also apply this approach to obtain a classification of maximal nilpotent...