Related papers: Polynomial Term Structure Models
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
We define and study the combinatorial properties of compositional Bernoulli numbers and polynomials within the framework of rational combinatorics.
In the first part of this note, we review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature. This notion hinges on how one defines the degree of a functor from…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising…
We investigate a family of permutation polynomials of finite fields of characteristic 2. Through a connection between permutation polynomials and quadratic forms, a general treatment is presented to characterize these permutation…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.
The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study is to provide some congruence relations satisfied by such quaternionic modular forms.
Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…
The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.
We give a survey of the analytic theory of matrix orthogonal polynomials.
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…
We define, for an arbitrary partially ordered set, a multi-variable polynomial generalizing the hook polynomial.
We discuss various aspects of representation of a polynomial as a sum of monomials (for example, uniqueness of such representation and related estimations).
In this document, we study the interaction between different geometric structures that can be defined as morphisms of sections of the generalized tangent bundle $\mathbb TM:= TM\oplus T^*M\to M$. In particular, we show the behaviour of…
We discuss several constructions of swap polynomials, that is 2--tensor valued matrix polynomials which are multiples of the swap or switch operator.