相关论文: Computation of Delta sets of numerical monoids

Let a polytope $P$ be defined by a system $A x \leq b$. We consider the problem of counting the number of integer points inside $P$, assuming that $P$ is $\Delta$-modular, where the polytope $P$ is called $\Delta$-modular if all the rank…

A set $S\subset\{1,2,...,n\}$ is called a Sidon set if all the sums $a+b~~(a,b\in S)$ are different. Let $S_n$ be the largest cardinality of the Sidon sets in $\{1,2,...,n\}$. In a former article, the author proved the following asymptotic…

Let $S \subset \mathbb{N}_0$ be a numerical monoid and let $\mathcal P_{\mathrm{fin}} (S)$, resp $\mathcal P_{\mathrm{fin},0}(S)$, denote the power monoid, resp. the restricted power monoid, of $S$, that is the set of all finite nonempty…

We introduce the concept of isolated factorizations of an element of a commutative monoid and study its properties. We give several bounds for the number of isolated factorizations of simplicial affine semigroups and numerical semigroups.…

In this paper, we determine minimal generating sets for several well-known monoids of matrices over semirings. In particular, we find minimal generating sets for the monoids consisting of: all $n\times n$ boolean matrices when $n\leq 8$;…

There are distributed graph algorithms for finding maximal matchings and maximal independent sets in $O(\Delta + \log^* n)$ communication rounds; here $n$ is the number of nodes and $\Delta$ is the maximum degree. The lower bound by Linial…

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 $H$,…

A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid $S$, consider the family of "shifted" monoids $M_n$ obtained by adding $n$ to each generator of $S$. In this paper, we characterize the…

Arithmetical congruence monoids, which arise in non-unique factorization theory, are multiplicative monoids $M_{a,b}$ consisting of all positive integers $n$ satsfying $n \equiv a \bmod b$. In this paper, we examine the asymptotic behavior…

In recent years codes that are not Uniquely Decipherable (UD) are been studied partitioning them in classes that localize the ambiguities of the code. A natural question is how we can extend the notion of maximality to codes that are not…

We call a depth-4 formula C set-depth-4 if there exists a (unknown) partition (X_1,...,X_d) of the variable indices [n] that the top product layer respects, i.e. C(x) = \sum_{i=1}^k \prod_{j=1}^{d} f_{i,j}(x_{X_j}), where f_{i,j} is a…

We analyze the set of increasingly enumerable additive submonoids of R, for instance, the set of logarithms of the positive integers with respect to a given base. We call them $\omega$-monoids. The $\omega$-monoids for which consecutive…

A set $A$ is MSTD (more-sum-than-difference) or sum-dominant if $|A+A|>|A-A|$, and is RSD (restricted-sum dominant) if $|A\hat{+}A|>|A-A|$, where $A\hat{+}A$ is the set of sums of distinct elements in $A$. We study an interesting family of…

Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the…

We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…

Let $G$ be a group. A subset $D$ of $G$ is a determining set of $G$, if every automorphism of $G$ is uniquely determined by its action on $D$. The determining number of $G$, denoted by $\alpha(G)$, is the cardinality of a smallest…

The $\Delta$-edge stability number ${\rm es}_{\Delta}(G)$ of a graph $G$ is the minimum number of edges of $G$ whose removal results in a subgraph $H$ with $\Delta(H) = \Delta(G)-1$. Sets whose removal results in a subgraph with smaller…

Let $A$ be a finite multiset of integers. If $B$ be a multiset such that $A$ and $B$ are $t$-complementing multisets of integers, then $B$ is periodic. We obtain the Biro-type upper bound for the smallest such period of $B$: Let…

We construct the $\Delta$ resonance as a superposition of a bare $\Delta$ state and the $\pi N$ continuum. It is parametrized by three coupling constants for local $\pi N \Delta$ and $\pi \pi N N$ couplings and the $\Delta$ mass. The latter…

Let $n = \mathrm{p}\!\cdot\!\mathrm{q}$ (p < q) and $\Delta = \lvert p-q \rvert$, where p,q are odd integers, then, it is hypothesized that factorizing this composite n will take O(1) time once the steady state value is reached for any…