相关论文: Generating subspace lattices, their direct product…

In this paper we study the cardinality of the dot product set generated by two subsets of vector spaces over finite fields. We notice that the results on the dot product problems for one set can be simply extended to two sets. Let E and F…

We prove that the minimal representation dimension of a direct product $G$ of non-abelian groups $G_1,\ldots,G_n$ is bounded below by $n+1$ and thereby answer a question of Ab\'ert. If each $G_i$ is moreover non-solvable, then this lower…

More than twenty-five years ago, Manickam, Mikl\'{o}s, and Singhi conjectured that for positive integers $n,k$ with $n \geq 4k$, every set of $n$ real numbers with nonnegative sum has at least $\binom{n-1}{k-1}$ $k$-element subsets whose…

Given positive linear functional l on a vector lattice L of real functions, and a vector subspace M of L, we construct a vector subspace P(M) of M in such a way that 1) l is nullcontinuous on P(M), and 2) if l is nullcontinuous on M then…

We study lattices in a product $G = G_1 \times \dots \times G_n$ of non-discrete, compactly generated, totally disconnected locally compact (tdlc) groups. We assume that each factor is quasi just-non-compact, meaning that $G_i$ is…

We prove that the rank (that is, the minimal size of a generating set) of lattices in a general connected Lie group is bounded by the co-volume of the projection of the lattice to the semi-simple part of the group. This was proved by…

Let $L$ be a lattice of full rank in $n$-dimensional real space. A vector in $L$ is called $i$-sparse if it has no more than $i$ nonzero coordinates. We define the $i$-th successive sparsity level of $L$, $s_i(L)$, to be the minimal $s$ so…

A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…

For a finite group $G$, let $d(G)$ denote the minimal number of elements required to generate $G$. In this paper, given a finite almost simple group $G$ and any maximal subgroup $H$ of $G$, we determine a precise upper bound for $d(H)$. In…

Given a connected graph $G$, a vertex $w\in V(G)$ strongly resolves two vertices $u,v\in V(G)$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A set $S$ of vertices is a strong metric…

We study the algebras of modular forms on type IV symmetric domains for simple lattices; that is, lattices for which every Heegner divisor occurs as the divisor of a Borcherds product. For every simple lattice $L$ of signature $(n,2)$ with…

A sublattice of the three-dimensional integer lattice $\mathbb Z^3$ is called cubic sublattice if there exists a basis of the sublattice whose elements are pairwise orthogonal and of equal lengths. We show that for an integer vector…

We consider graded rings $R$ generated by $n$ homogeneous elements of positive integer degrees $w_1, \ldots, w_n$ that have least common multiple $d$. We show that for every integer $k \geq \max(1, n-2)$, the $kd$th Veronese subring…

Let V be an infinite matrix with rows and columns indexed by the positive integers, and entries in a field F. Suppose that v_{i,j} only depends on i-j and is 0 for |i-j| large. Then V^n is defined for all n, and one has a "generating…

A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. We show that the 6-element Brandt monoid generates a finitely universal variety of monoids and, by the previous results, it…

In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N)…

The lattice path model suggested by E. Deutsch is derived from ordinary Dyck paths, but with additional down-steps of size -3,-5,-7,... . For such paths, we find the generating functions of them, according to length, ending at level $i$,…

We define two a priori tests of pseudo-random number generators for the class of linear matrix-recursions. The first desirable property of a random number generator is the smallness of serial or lagged correlations between generated…

We prove that for a number field $F$, the distribution of the points of a set $\Sigma \subset \mathbb{A}_F^n$ with a purely exponential parametrization, for example a set of matrices boundedly generated by semi-simple (diagonalizable)…

The simple cubic lattice defines a set of points at regular distances. The volume of the Voronoi cells around each point may serve as a weight for integration over the entire space. We add interstitial points to this grid according to the…