S. Tringali

activity

20122023

most citedPower monoids: A bridge between Factorization Theory and Arithmetic Combinatorics

56 citations · 322 across the 35 of their papers we have counts for

collaborators

35 papers

math.CO2023★ 8 cited

A conjecture by Bienvenu and Geroldinger on power monoids

Salvatore Tringali, Weihao Yan

Let $S$ be a numerical monoid, i.e., a submonoid of the additive monoid $(N, +)$ of non-negative integers such that $N ∖ S$ is finite. Endowed with the oper…

math.FA2023

Subcommutativity of integrals and quasi-arithmetic means

Dorota Glazowska, Paolo Leonetti, Janusz Matkowski +1

Let $(X, L, λ)$ and $(Y, M, μ)$ be finite measure spaces for which there exist $A \in L$ and $B \in M$ with either $0 < λ (A) < 1 < λ (X)$ and…

math.RA2023★ 6 cited

On the finiteness of certain factorization invariants

Laura Cossu, Salvatore Tringali

Let $H$ be a monoid, $F (X)$ be the free monoid on a set $X$ , and $π_{H}$ be the unique extension of the identity map on $H$ to a monoid homomorphism $F (H) \to H$ . G…

math.NT2022★ 3 cited

On the density of sumsets, II

Paolo Leonetti, Salvatore Tringali

Arithmetic quasi-densities are a large family of real-valued set functions partially defined on the power set of $N$ , including the asymptotic density, the Banach density,…

math.RA2022★ 10 cited

A characterization of atomicity

Salvatore Tringali

In [Math. Proc. Cambridge Philos. Soc. 64 (1968), 251-264], P.M. Cohn famously claimed that a commutative domain is atomic if and only if it satisfies the ascending chain condition…

math.RA2022★ 15 cited

Factorization under Local Finiteness Conditions

Laura Cossu, Salvatore Tringali

It has been recently observed that fundamental aspects of the classical theory of factorization can be greatly generalized by combining the languages of monoids and preorders. This…

math.RA2021★ 12 cited

Abstract Factorization Theorems with Applications to Idempotent Factorizations

Laura Cossu, Salvatore Tringali

Let $⪯$ be a preorder on a monoid $H$ and $s$ be an integer $\geq 2$ . The $⪯$ -height of an $x \in H$ is the sup of the integers $k \geq 1$ for which there is a (strictly)…

math.RA2021★ 22 cited

An Abstract Factorization Theorem and Some Applications

Salvatore Tringali

We combine the language of monoids with the language of preorders so as to refine some fundamental aspects of the classical theory of factorization and prove an abstract factorizat…

math.RA2020★ 1 cited

Factorization in monoids and rings

Salvatore Tringali

Let $H^{\times}$ be the group of units of a multiplicatively written monoid $H$ . We say $H$ is acyclic if $x y z \neq = y$ for all $x, y, z \in H$ with $x \in / H^{\times}$ or $z \notin H^…

math.NT2020★ 8 cited

On the density of sumsets

Paolo Leonetti, Salvatore Tringali

Recently introduced by the authors in [Proc. Edinb. Math. Soc. 60 (2020), 139-167], quasi-densities form a large family of real-valued functions partially defined on the power set…

math.NT2019

A generalization to number fields of Euler's theorem on the series of reciprocals of primes

Salvatore Tringali

Let $X$ be a set of positive integers, and let $Z_{K}$ be the ring of integers of a number field $K$ of degree $n$ . Denote by $N (I)$ the absolute norm of an ideal $I$ of $\ma…

math.AC2019★ 6 cited

On half-factoriality of transfer Krull monoids

Weidong Gao, Chao Liu, Salvatore Tringali +1

Let $H$ be a transfer Krull monoid over a subset $G_{0}$ of an abelian group $G$ with finite exponent. Then every non-unit $a \in H$ can be written as a finite product of atoms, say $…

math.AC2019★ 40 cited

On strongly primary monoids, with a focus on Puiseux monoids

Alfred Geroldinger, Felix Gotti, Salvatore Tringali

Primary and strongly primary monoids and domains play a central role in the ideal and factorization theory of commutative monoids and domains. It is well-known that primary monoids…

math.NT2019

On Small Sets of Integers

Paolo Leonetti, Salvatore Tringali

An upper quasi-density on $H$ (the integers or the non-negative integers) is a real-valued subadditive function $μ^{*}$ defined on the whole power set of $H$ such that…

math.RA2018★ 22 cited

On the Arithmetic of Power Monoids and Sumsets in Cyclic Groups

Austin A. Antoniou, Salvatore Tringali

Let $H$ be a multiplicatively written monoid with identity $1_{H}$ (in particular, a group). We denote by $P_{fin, \times} (H)$ the monoid obtained by endowing the collect…

math.NT2017★ 27 cited

Structural properties of subadditive families with applications to factorization theory

Salvatore Tringali

Let $H$ be a multiplicatively written monoid. Given $k \in N^{+}$ , we denote by $U_{k}$ the set of all $ℓ \in N^{+}$ such that $a_{1} \dots a_{k} = b_{1} \dots b_{ℓ}$ for so…

math.CA2017★ 7 cited

Commutativity of integral quasi-arithmetic means on measure spaces

Dorota Głazowska, Paolo Leonetti, Janusz Matkowski +1

Let $(X, L, λ)$ and $(Y, M, μ)$ be finite measure spaces for which there exist $A \in L$ and $B \in M$ with $0 < λ (A) < λ (X)$ and $0 < μ(B)…

math.NT2017★ 56 cited

Power monoids: A bridge between Factorization Theory and Arithmetic Combinatorics

Yushuang Fan, Salvatore Tringali

We extend a few fundamental aspects of the classical theory of non-unique factorization, as presented in Geroldinger and Halter-Koch's 2006 monograph on the subject, to a non-commu…

math.AC2016★ 21 cited

Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules

Yushuang Fan, Alfred Geroldinger, Florian Kainrath +1

Let $H$ be a commutative semigroup with unit element such that every non-unit can be written as a finite product of irreducible elements (atoms). For every $k \in N$ , let $…

math.CO2016★ 3 cited

Multivariate Delta Goncarov and Abel Polynomials

Rudolph Lorentz, Salvatore Tringali, Catherine H. Yan

Classical Gončarov polynomials are polynomials which interpolate derivatives. Delta Gončarov polynomials are polynomials which interpolate delta operators, e.g., forward and backwa…

math.CO2016

Cauchy-Davenport type inequalities, I

Salvatore Tringali

Let $G = (G, +)$ be a group (either abelian or not). Given $X, Y \subseteq G$ , we denote by $⟨ Y ⟩$ the subsemigroup of $G$ generated by $Y$ , and we set…

math.CO2015★ 7 cited

Generalized Goncarov polynomials

Rudolph Lorentz, Salvatore Tringali, Catherine H. Yan

We introduce the sequence of generalized Gončarov polynomials, which is a basis for the solutions to the Gončarov interpolation problem with respect to a delta operator. Explicitly…

math.NT2015

On the number of distinct prime factors of a sum of super-powers

Paolo Leonetti, Salvatore Tringali

Given $k, ℓ \in N^{+}$ , let $x_{i, j}$ be, for $1 \leq i \leq k$ and $0 \leq j \leq ℓ$ , some fixed integers, and define, for every $n \in N^{+}$ , $s_n := \sum_{i=1}^k \pro…

math.CA2015★ 9 cited

Upper and lower densities have the strong Darboux property

Paolo Leonetti, Salvatore Tringali

Let $P (N)$ be the power set of $N$ . An upper density (on $N$ ) is a non\-decreasing and subadditive function $μ^{*} : P (N) \to R$ such that…