相关论文: A new partition identity coming from complex dynam…
In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and…
In a recent paper, Carrell and Goulden found a combinatorial identity of the Bernstein operators that they then used to prove Bernstein's Theorem. We show that this identity is a straightforward consequence of the classical result. We also…
We obtain a new family of relations satisfied by the partition function. In contrast with most partition relations, these involve non-trivial roots of unity. We present two proofs, one using the fact that the discriminant modular form is a…
We show how certain suitably modified N-modular diagrams of integer partitions provide a nice combinatorial interpretation for the general term of Zeilberger's KOH identity. This identity is the reformulation of O'Hara's famous proof of the…
Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a theorem of Borodin. Here, we extend this framework to include…
We use the celebrated circle method of Hardy and Ramanujan to develop convergent formulae for counting a restricted class of partitions that arise from the G\"ollnitz--Gordon identities.
Extending the notion of $r$-(class) regular partitions, we define $(r_{1},...,r_{m})$-class regular partitions. A partition identity is presented and described by making use of the Glaisher correspondence.
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…
Based on a bijection due to Fu and Tang, we provide combinatorial proofs of several partition identities of Andrews and Merca. We also introduce two weights for partitions to extend one of these identities.
A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…
The decimal expansion real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
Starting with a combinatorial partition theorem for words over an infinite alphabet dominated by a fixed sequence, established recently by the authors, we prove recurrence results for topological dynamical systems indexed by such words. In…
We give bijective proofs using Fomin's growth diagrams for identities involving numbers of vacillating tableaux that arose in the representation theory of partition algebras or are inspired by such identities.
A new construction of the real number system, that is built directly upon the additive group of integers and has its roots in the definition due to Henri Poincar\'e of the rotation number of an orientation preserving homeomorphism of the…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
We study divide-and-conquer recurrences of the form \begin{equation*} f(n) = \alpha f(\lfloor \tfrac n2\rfloor) + \beta f(\lceil \tfrac n2\rceil) + g(n) \qquad(n\ge2), \end{equation*} with $g(n)$ and $f(1)$ given, where $\alpha,\beta\ge0$…
We give a proof of a recent combinatorial conjecture due to the first author, which was discovered in the framework of commutative algebra. This result gives rise to new companions to the famous Andrews-Gordon identities. Our tools involve…