Related papers: Minimal counting systems and commutative monoids
We give an elementary proof of a monotone selection principle which allows to pass from increasing nets to increasing sequences in the Hermitian part of a $\sigma$-finite von Neumann algebra. This is to be seen as a ``monotone version'' of…
Dismal arithmetic is just like the arithmetic you learned in school, only simpler: there are no carries, when you add digits you just take the largest, and when you multiply digits you take the smallest. This paper studies basic number…
We give an overview of the existing algorithms to compute nonunique factorization invariants in finitely generated monoids.
Given a finite Markov chain, we investigate the first minors of the transition matrix of a lifting of this Markov chain to covering trees. In a simple case we exhibit a nice factorisation of these minors, and we conjecture that it holds…
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the…
We introduce an intuitionistic modal logic strictly contained in the intuitionistic modal logic IK and being an appropriate candidate for the title of ``minimal normal intuitionistic modal logic''.
We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
These notes, associated with a topics course, are concerned with some general methods related to norms and linear transformations.
Normal and composition series of modules enumerated by ordinal numbers are studied. The Jordan-Holder theorem for them is discussed.
Computations in the cohomology of finite groups.
This paper presents two enumeration techniques based on Hilbert functions. The paper illustrates these techniques by solving two chessboard problems.
The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations…
We discuss some examples that illustrate the countability of the positive rational numbers and related sets. Techniques include radix representations, Godel numbering, the fundamental theorem of arithmetic, continued fractions, Egyptian…
Given a monoid $H$ (written multiplicatively), the family $\mathcal{P}_{\mathrm{fin},1}(H)$ of all non-empty finite subsets of $H$ containing the identity element $1_H$ is itself a monoid, called the reduced finitary power monoid of $H$,…
Counting the number of models of a Boolean formula is a fundamental problem in artificial intelligence and reasoning. Minimal models of a Boolean formula are critical in various reasoning systems, making the counting of minimal models…