Related papers: Disquisitiones 235
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
In this article we show how the Dedekind-Hasse criterion may be applied to prove a simple result about quadratic number fields that usually is derived as a consequence of the theory of ideals and ideal classes.
We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
We report on experience with an investigation of the analytic structure of the solution of certain algebraic complex equations. In particular the behavior of their series expansions around the origin is discussed. The investigation imposes…
In this paper, we present a generalization of one of the theorems in [G. E. Andrews, Partitions with parts separated by parity, \textit{Annals of Combinatorics} \textbf{23}(2019), 241 - 248], and give its bijective proof. Further variations…
We introduce the existence of a Genus-Type Theory that generalizes classical genus theory by linking fractional ideals of number fields to structures built from their Galois groups and associated Diophantine equations, as formally stated in…
We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…
In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by…
Cubic forms in three variables are parametrised by points of $\P^9$. We study the subvarieties in this space defined by decomposable forms. Specifically, we calculate the equivariant minimal resolutions of these varieties and describe their…
We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be universal if it contains a quadratic subform that is…
We give improved bounds for our theorem in [GW09], which shows that a system of linear forms on $\mathbb{F}_p^n$ with squares that are linearly independent has the expected number of solutions in any linearly uniform subset of…
This text consists of the introduction, table of contents, and bibliography of a long manuscript (703 pages) that is currently submitted for publication. This manuscript develops an extension of Garside's approach to braid groups and…
This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield…
In this chapter are given necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials. In addition, we also present the functional Rodrigues…
We construct a tangent-obstruction theory for Azumaya algebras equipped with a quadratic pair. Under the assumption that either 2 is a global unit or the algebra is of degree 2, we show how the deformation theory of these objects reduces to…
Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in…
On the basis of what I call physico-formalist philosophy of mathematics, I will develop an amended account of the Kantian--Reichenbachian conception of constitutive a priori. It will be shown that the features (attributes, qualities,…
We show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra…
We derive properties and a characterization of discrete composition matrices which are useful in the field of numerical computation of shape correspondences.