A quasi-symmetric design is a (v, k, λ) design with two intersection numbers x, y where 0 ≤ x < y < k. We show that for fixed x, y, λ with x > 1, λ > 1, y = λ and λ (4xy + ((y − x) − 2x− 2y + 1)λ) a perfect square of a positive integer, there exist finitely many quasi-symmetric designs. We rule out the possibilities of quasi-symmetric designs corresponding to y = x + 3 and (λ, x) = (9, 2), (8, ...

Abstract. In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions, in particular as they form a subalgebra of the algebra of symmetric functions. This subalgebra is generated by the odd power sum symmetric functions...

and Applied Analysis 3 We will prove this theorem by contradiction. The idea is similar to the proof of Theorem 1. Suppose ψ is a rotationally symmetric harmonic diffeomorphism from P(a) onto D∗ with the metric σ 2 d|u|, with the form ψ = g(r)e, then substituting ψ, σ 2 to u, σ in (2), respectively, we can get

Let n > 1 be an integer and let Bn denote the hyperoctahedral group of rank n. The group Bn acts on the polynomial ring Q[x1, . . . , xn, y1, . . . , yn] by signed permutations simultaneously on both of the sets of variables x1, . . . , xn and y1, . . . , yn. The invariant ring MBn := Q[x1, . . . , xn, y1, . . . , yn]n is the ring of diagonally signedsymmetric polynomials. In this article, we p...

We present new lower bounds for the symmetric border rank of the n × n determinant for all n. Further lower bounds are given for the 3 × 3 permanent.

In this paper we study a class of symmetric polynomial differential systems in R3, which has a set of parallel invariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints at infinity. The global study near infinity is performed using the Poincaré compactification. We prove that for all n ∈ N there is εn > 0 such that for 0 < ε < εn the system has at...

We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence pk+1 = xpk − ckpk−1, with a nondecreasing sequence {ck}. As a special case they include a non-asymptotic version of Máté, Nevai and Tot...