Related papers: On the Linear AFL: The Non-Basic Case

In two-dimensional models of critical non-intersecting loops, there are $\ell$-leg fields that insert $\ell\in\mathbb{N}^*$ open loop segments, and diagonal fields that change the weights of closed loops. We conjecture an exact formula for…

Let $S_n$ be the symmetric group on $n$ points. Deza and Frankl [M. Deza and P. Frankl, On the maximum number of permutations with given maximal or minimal distance, J. Combin. Theory Ser. A 22 (1977) 352--360] proved that if ${\cal F}$ is…

The Fundamental Theorem of Algebra can be thought of as a statement about the real numbers as a space, considered as an algebraic set over the real numbers as a field. This paper introduces what it means for an algebraic set or affine…

We reduce the principal problem of Additive Number Theory of whether an infinite sequence of integers constitutes a finite basis for the integers to a Diophantine problem involving the difference set of the sequence, by proving a formula…

Lame equation arises from deriving Laplace equation in ellipsoidal coordinates; in other words, it's called ellipsoidal harmonic equation. Lame functions are applicable to diverse areas such as boundary value problems in ellipsoidal…

For a real affine hyperplane arrangement, we define an integer intersection matrix with a natural $q$-deformation related to the intersections of bounded chambers of the arrangement. By connecting the integer matrix to a bilinear form of…

A lattice $L$ is said lowly finite if the set $[\mathsf{0},a]$ is finite for every element $a$ of $L$. We mainly aim to provide a complete proof that, if $M$ is a subset of a complete lowly finite distributive lattice $L$ containing its…

For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental…

In the setting of modern mathematical logic and model theory, classification theory has been one of the landmark achievements of the field. Likewise, the classification of UHF-algebras and AF-algebras were substantial contributions to the…

As an analog to the Jacquet-Rallis fundamental lemma that appears in the relative trace formula approach to the Gan-Gross-Prasad conjectures, the arithmetic fundamental lemma was proposed by Wei Zhang and used in an approach to the…

This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what…

We generalize I. Frenkel's orbital theory for non twisted affine Lie algebras to the case of twisted affine Lie algebras using a character formula for certain non-connected compact Lie groups.

Persistence of non-degeneracy is a phenomenon which appears in the theory of $\overline{\mathbb Q}_l$-representations of the linear group: every irreducible submodule of the restriction to the mirabolic sub-representation of a…

The aim of this article is to generalize logics of formal inconsistency ($\textbf{LFI}$s) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible…

Recently, great attention has been focused on the study of fractional and non-local operators of elliptic type, both for pure mathematical research and in view of concrete real-world applications. Our problem is related to the fractional…

A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of…

A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex…

We unify Linear Algebra by proposing a definition of determinants via one equation that implies all known properties of them:\\ 1. Cramer's Rule,\\ 2. Cofactor expansion,\\ 3. Antisymmetry of determinants,\\ 4. Linearity of determinants,\\…

Let X be an algebraic curve over Q and t a non-constant Q-rational function on X such that Q(t) is a proper subfield of Q(X). For every integer n pick a point P_n on X such that t(P_n)=n. We conjecture that, for large N, among the number…

The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a…