Let G be a transitive permutation group of degree n. We say that G is 2′elusive if n is divisible by an odd prime, but G does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive 2′-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate autom...

We give equivalent conditions for a monomial sequence to be a dsequence or a proper sequence, and a sufficient condition for a monomial sequence to be an s-sequence in order to compute invariants of the symmetric algebra of the ideal generated by it.

A large class of Boolean functions, as well as almost all symmetr ic Boolean functions, are shown to have no two-level completely robust path-delay-fault testable ( R P D F T ) realization b y combinational circuits. Exact and asymptotic formulae are derived fo r the number of symmetric Boolean functions which have two-level completely R P D F T realization. To achieve completely R P D F T real...

Let wλ x : 1 − x2 λ−1/2 and Pλ,n x be the ultraspherical polynomials with respect to wλ x . Then, we denote the Stieltjes polynomials with respect to wλ x by Eλ,n 1 x satisfying ∫1 −1 wλ x Pλ,n x Eλ,n 1 x x dx 0, 0 ≤ m < n 1, ∫1 −1 wλ x Pλ,n x Eλ,n 1 x xdx / 0, m n 1. In this paper, we investigate asymptotic properties of derivatives of the Stieltjes polynomials Eλ,n 1 x and the product Eλ,n 1 ...

Let X be a projective manifold of dimension n, a symmetric differential of degree m is a section of the m-th symmetric power of the sheaf of holomorphic 1-forms, SΩX . A symmetric differential w of degree m is of rank 1 if it can be locally written in the form w|U = fμ, where μ ∈ H(U,ΩX) and f ∈ O(U). Symmetric differentials of degree 1, i.e. holomorphic 1-forms, are trivially of rank 1. Holomo...

Using cocommutativity of the Hopf algebra of symmetric functions, certain skew Schur functions are proved to be equal. Some of these skew Schur function identities are new.

By means of comp lete symmetric polynomials this paper gives a new proof for the Vander-monde determinant formula. Another alternative proof for this formula is obtained via the collocatio n matrices. It also gives a generalized relationship between the Vandermo nde, the Pascal and the Stirling matrices. A new app roach to obtain the explicit inverse of the Vandermo nde matrix is investigated. ...

We study the moments of the symmetric power L-functions of primitive forms at the edge of the critical strip twisted by the square of the value of the standard L-function at the center of the critical strip. We give a precise expansion of the moments as the order goes to infinity. CONTENTS

Using symmetric algebras we simplify (and slightly strengthen) the Bruns-Eisenbud-Evans “generalized principal ideal theorem” on the height of order ideals of nonminimal generators in a module. We also obtain a simple proof and an extension of a result by Kwieciński, which estimates the height of certain Fitting ideals of modules having an equidimensional symmetric algebra.