Related papers: Small generators of function fields

Let G=SL_3(Z/pZ), p a prime. Let A be a set of generators of G. Then A grows under the group operation. To be precise: denote by |S| the number of elements of a finite set S. Assume |A| < |G|^{1-\epsilon} for some \epsilon>0. Then |A\cdot…

The rank of a finite semigroup is the smallest number of elements required to generate the semigroup. A formula is given for the rank of an arbitrary (non necessarily regular) Rees matrix semigroup over a group. The formula is expressed in…

In the present work, we determine explicitly the genus of any separable cubic extension of any global function field given the minimal polynomial of the extension. We give algorithms computing the ramification data and the genus of any…

In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…

In this paper we find the genus field of finite abelian extensions of the global rational function field. We introduce the term conductor of constants for these extensions and determine it in terms of other invariants. We study the…

In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…

We provide sufficient conditions on the components of a vector field, which ensure the existence of Dulac functions depending on special functions for such vector field. We also present some applications and examples in order to illustrate…

We prove that a weak factorization system on a locally presentable category is accessible if and only if it is small generated in the sense of R. Garner. Moreover, we discuss an analogy of Smith's theorem for accessible model categories.

Semigroups describing the time evolution of open quantum systems in finite dimensional spaces have generators of a special form, known as Lindblad generators. The simple generators, characterized by only one operator, are analyzed. The…

We investigate finite field extensions of the unital 3-field, consisting of the unit element alone, and find considerable differences to classical field theory. Furthermore, the structure of their automorphism groups is clarified and the…

Let $\mathcal{A}$ be an essentially small abelian category. We prove that if $\mathcal{A}$ admits a generator $M$ with ${\rm End}_{\mathcal{A}}(M)$ right artinian, then $\mathcal{A}$ admits a projective generator. If $\mathcal{A}$ is…

For a finite separable field extension K/k, all subfields can be obtained by intersecting so-called principal subfields of K/k. In this work we present a way to quickly compute these intersections. If the number of subfields is high, then…

Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…

The joint use of counting functions, Hilbert basis and Markov basis allows to define a procedure to generate all the fractions that satisfy a given set of constraints in terms of orthogonality. The general case of mixed level designs,…

For an ergodic probability-measure-preserving action $G \curvearrowright (X, \mu)$ of a countable group $G$, we define the Rokhlin entropy $h_G^{\mathrm{Rok}}(X, \mu)$ to be the infimum of the Shannon entropies of countable generating…

We present an off-shell generating function for all cubic interactions of Higher Spin gauge fields constructed in arXiv:1003.2877. It is a generalization of the on-shell generating function proposed in arXiv:1006.5242, is written in a very…

We introduce a model of simple type theory with potential infinite carrier sets. The functions in this model are automatically continuous, as defined in this paper. This notion of continuity does not rely on topological concepts, including…

We derive basic properties of minimal extensions of local rings and their restrictions to subrings. Some applications are included to subrings of truncated polynomial rings.

Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.

Let $D$ be a large category which is cocomplete. We construct a model structure (in the sense of Quillen) on the category of small functors from $D$ to simplicial sets. As an application we construct homotopy localization functors on the…