Related papers: Generalized Foster's identities
We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct…
We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums.…
We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of…
We introduce the concept of indexed identity, where the usual notion of identity is a particular case. Our mathematical framework allows us a generalized method for `indexing' predicates, which corresponds to `fuzzification' of properties,…
An important goal in studying the relations between unitary VOAs and conformal nets is to prove the equivalence of their ribbon categories. In this article, we prove this conjecture for many familiar examples. Our main idea is to construct…
In this note, we show how a combinatorial identity of Frisch can be applied to prove and generalize some well-known identities involving harmonic numbers. We also present some combinatorial identities involving odd harmonic numbers which…
Starting from the characteristic polynomial for ordinary matrices we give a combinatorial deduction of the Mandelstam identities and viceversa, thus showing that the two sets of relations are equivalent. We are able to extend this…
A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
Extending work of Foster, Doyle, and others, we show how the Foster Theorems, a family of results concerning effective resistances on finite graphs, can in certain cases be extended to infinite graphs. A family of sum rules is then…
New integral identities satisfied by topological solitons in a range of classical field theories are presented. They are derived by considering independent length rescalings in orthogonal directions, or equivalently, from the conservation…
This work focuses on the identifiability of dynamical networks with partial excitation and measurement: a set of nodes are interconnected by unknown transfer functions according to a known topology, some nodes are subject to external…
Interest in studying the conductive properties of networks made from randomly distributed nanowires is due to their numerous technological applications. Although the sheet resistance of such networks can be calculated directly, the…
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this…
In this paper, we show how informativity and identifiability for networks of dynamical systems can be investigated using Gr\"obner bases. We provide a sufficient condition for informativity in terms of positive definiteness of the spectrum…
We derive some Fibonacci and Lucas identities which contain inverse binomial coefficients. Extension of the results to the general Horadam sequence is possible, in some cases.
In this note we present a method for obtaining a wide class of combinatorial identities. We give several examples, in particular, based on the Gamma and Beta functions. Some of them have already been considered by previously, and other are…