Related papers: Minimal counting systems and commutative monoids
The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
Compositional minimisation can be an effective technique to reduce the state space explosion problem. This technique considers a parallel composition of several processes. In its simplest form, each sequential process is replaced by an…
Reconciliation of frequentist and Bayesian approaches to elementary treatment of data in nuclear and particle physics is attempted. Unique procedure to express the significance of a small count in presence of background is henceforth…
A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatorially finite, cancellative, commutative monoids to be…
We give an elementary proof of the development of Macdonald polynomials in terms of "modified complete" and elementary symmetric functions.
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…
We give a simple recursive formula to obtain the general sum of the first $N$ natural numbers to the $r$th power. Our method allows one to obtain the general formula for the $(r+1)$th power once one knows the general formula for the $r$th…
The aim of this note, which raises more questions than it answers, is to study natural operations acting on the cohomology of various types of algebras. It contains a lot of very surprising partial results and examples.
The main purpose of this note is to provide a topological approach to defining additive functions on Riemannian co-compact normal coverings.
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
We discuss how countable subadditivity of operators can be derived from subadditivity under mild forms of continuity, and provide examples manifesting such circumstances.
We construct a recursive formula for a complete system of primitive orthogonal idempotents for any $R$-trivial monoid. This uses the newly proved equivalence between the notions of $R$-trivial monoid and weakly ordered monoid.
In this short note, we give basic enumerative results on colored integer partitions.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
Nonunique factorization in commutative monoids is often studied using factorization invariants, which assign to each monoid element a quantity determined by the factorization structure. For numerical monoids (co-finite, additive submonoids…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
This note contains a simple construction of complete sets of MUBs, using bent functions to write the new basis vectors as explicit linear combinations of the standard basis.
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.