Related papers: Partial combinatory algebra and generalized number…
We look at generalized complex structures from the point of view of Poisson and Dirac geometry and we remark that the puzzling equations underlying the notion of generalized complex structure have miraculously simple meaning when passing to…
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…
Let $\alpha$ and $\beta$ be two nonnegative integers such that $\beta < \alpha$. For an arbitrary sequence $\{a_n\}_{n\geqslant 1}$ of complex numbers, we consider the generalized Lambert series in order to investigate linear combinations…
We generalize the definition of a counter and counter reversal complexity and investigate the power of generalized deterministic counter automata in terms of language recognition.
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions…
Generalized correlation analysis (GCA) is concerned with uncovering linear relationships across multiple datasets. It generalizes canonical correlation analysis that is designed for two datasets. We study sparse GCA when there are…
We introduce the notion of Lie algebras with plus-minus pairs as well as regular plus-minus pairs. These notions deal with certain factorizations in universal enveloping algebras. We show that many important Lie algebras have such pairs and…
We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing…
We establish a condition (so called generalized entropic property), equivalent to the fact that for every algebra A from a given variety V, the set of all subalgebras of A is a subuniverse of the complex algebra of A. We investigate the…
In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (and of Stirling numbers of the second kind) that appears to be relevant to the so-called Boson normal ordering problem. They provided a…
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
The classical derangement numbers count fixed point-free permutations. In this paper we study the enumeration problem of generalized derangements, when some of the elements are restricted to be in distinct cycles in the cycle decomposition.…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on…
We describe a type of Lie color algebra, which we call generic, whose universal enveloping algebra is a domain with finite global dimension. Moreover, it is an iterated Ore extension. We provide an application and show Grobner basis methods…
Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way.…
We present here some new identities for generalizations of Fibonacci and Lucas numbers by combinatorially interpreting these numbers in terms of numbers of certain tilings of a $1 \times m$ board. As a consequence, some new interesting…
In this study we introduce a second type of higher order generalised geometric polynomials. This we achieve by examining the generalised stirling numbers $S(n; k;\alpha;\beta;\gamma)$ [Hsu & Shiue,1998] for some negative arguments. We study…