Related papers: Frobenius Splittings

We formulate some conjectures that relates semisimple Frobenius manifolds, their spectral curves and integrable hierarchies.

We study the structure of the family of numerical semigroups with fixed multiplicity and Frobenius number. We give an algorithmic method to compute all the semigroups in this family. As an application we compute the set of all numerical…

Alternative approaches to Lebesgue integration are considered.

The Jacobian algebras are introduced and their various properties are studied.

In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.

Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian…

This is brief and hopefully friendly, with basic notions, a few different perspectives, and references with more information in various directions.

Necessary and sufficient conditions for some deformation algebras to provide formal Frobenius structures are given. Also, examples of formal Frobenius structures with fundamental tensor that is not of the deformation type and examples of…

In the study of group determinants, Frobenius introduced certain partial differential operators. This paper presents several results concerning the invariant rings derived from these partial differential operators.

In this introductory paper we study nearly Frobenius algebras which are generalizations of the concept of a Frobenius algebra which appear naturally in topology: nearly Frobenius algebras have no traces (co-units). We survey the most basic…

We show that for large instances the order of magnitude of the expected Frobenius number is (up to a constant depending only on the dimension) given by its lower bound.

We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.

In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.

I discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method.

We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.

These notes are based on a sequence of five lectures given to graduate students. The main goal is to prove the so-called Painleve property for semi-simple Frobenius manifolds.

A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current…

In this paper, we give some sufficient conditions for a $n$-dimensional rectangle to be tiled with a set of bricks. These conditions are obtained by using the so-called Frobenius number.

Following the program of algebraic Frobenius splitting begun by Kumar and Littelmann, we use representation-theoretic techniques to construct a Frobenius splitting of the cotangent bundle of the flag variety of a semisimple algebraic group…

The purpose of this paper is to give a complete derivation of the limiting distribution of large Frobenius numbers outlined in earlier work of J. Bourgain and Ya. Sinai and fill some gaps formulated there as hypotheses.