Spectral analysis on the symmetric group Sn calls for computing projections of functions deened on Sn and its homogeneous spaces, onto invariant subspaces. In particular, for the analysis of partially ranked data, the appropriate homogeneous spaces are given as quotients by Young subgroups. Here the naive character theoretic approach to computing projections requires O(n n!) operations. In this...

A-hypergeometric systems are systems of linear partial differential equations with polynomial coefficients that can be built out of a toric ideal and a parameter vector. Homogeneous toric ideals are themselves built out of combinatorial data, n distinct integer points lying in a hyperplane off the origin in d-dimensional space. We may assume that these points are the columns of a d×n integer ma...

Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non-homogeneous algorithms.1 Although both classes contain algorithms with worst and best cases, homogeneous algorithms behave uniformly on all instances. This partition clarifies in a completely mathematical way the previously ment...

Homogeneous and heterogeneous types of catalysis are frequently considered as separate disciplines or even opposed to each other. In the present work, a new type mixed hetero-/homogeneous was demonstrated for case selective alkylarene oxidation by molecular oxygen. The proposed catalytic system consists two widely available components: N-hydroxyphthalimide (NHPI, homogeneous organocatalyst free...

– In Diophantine Approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that the exponent of approximation to a generic point in R n by a system of n linear forms is equal to the inverse of the uniform homogeneous exponent associate...

Abstract. Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A) = lim sup n→∞ n √ an, where an is the vector space dimension of the n’th homogeneous component. When A is the homogeneous quotient of a finitely generated free associative algebra, they showed that H(A) ≤ √ a2. Using some results of Friedland on the maximal spectral radius of (0, 1)-matrices wit...

Let K be an algebraically closed field. For n ≥ 0, let An denote Kn, and let A = K[An] denote K[X1, . . . , Xn]. We refer to An as affine n-space. For any subset S ⊆ An, let I(S) ⊆ A denote the ideal of all polynomials that vanish on S. (For those familiar with Spec, the affine scheme associated to S is Spec(A/I(S)). Note that any ideal I ⊆ A defines an affine subscheme of Spec(A), and ideals I...

Let {f0, · · · , fn; g0, · · · , gn} be a sequence of homogeneous polynomials in 2n + 2 variables with no common zeroes in P and suppose that the degrees of the polynomials are such that Q = ∑n i=0 figi is a homogeneous polynomial. We shall refer to the hypersurface X defined by Q as a generalized quadric. In this note, we prove that generalized quadrics in P C for n ≥ 1 are reduced.

Let {f0, · · · , fn; g0, · · · , gn} be a sequence of homogeneous polynomials in 2n + 2 variables with no common zeroes in P and suppose that the degrees of the polynomials are such that Q = ∑n i=0 figi is a homogeneous polynomial. We shall refer to the hypersurface X defined by Q as a generalised quadric. In this note, we prove that generalised quadrics in P C for n ≥ 1 are reduced.