arXiv subjects

João Victor Monteiros de Andrade

Publications and source records attributed to João Victor Monteiros de Andrade.

4 recordsLinked to original sources

arXiv2026

Proportion of Simple Subgroups in Finite Groups and Their Applications

This work introduces and investigates the function $ \mathcal{V}(G) = \frac{\text{Simp}(G)}{|L(G)|} $, where $ \text{Simp}(G) $ denotes the number of simple subgroups and $ |L(G)| $ the total number of subgroups of a finite group $ G $. The function $ \mathcal{V}(G) $, defined on the interval $ [0,1] $, represents the proportion of simple subgroups relative to the total number of subgroups. It serves as a tool for analyzing structural patterns in finite groups, particularly in p-groups and other families.

math.GR↗

arXiv2026

Finite products in commutative monoids: well-definition, recursion on finite subsets, and why the empty product is $1$

The convention "empty product $=1$" is ubiquitous in mathematics, but often appears without an explicit structural justification. This note provides a self-contained reference to this fact in the context of commutative monoids. We construct the product of an indexed family by a finite set, prove its enumeration independence, and show that it is uniquely characterized by a recursion scheme in Fin$(I)$: value in the empty set and insertion rule of a new index. In particular, the value of the empty product is necessarily the neutral element $1$. We further record two complementary and independent justifications of this fact: one via the list-free monoid and another via distributive identities in semi-rings. Next, we formulate the same phenomenon in universal terms by means of the commutative multiset-free monoid of finite support. We also discuss partially commutative extensions, via trace monoids and heaps, and include brief applications in linear algebra, survival statistics, category theory, and analysis. The corresponding additive version recovers, by the same principle, the identity "empty sum $=0$".

math.RA↗

arXiv2025

A note on connecting multiplicative functions defined on finite groups

In the present work we explore relationships between multiplicative functions defined in \cite{Garonzi_2018}, \cite{Lazorec}. To do so, we use other important quotients defined and studied in \cite{ndeg}, \cite{Marius}, thus establishing deeper connections that were previously little or not evaluated in some group families. Furthermore, we extract new characterizations and asymptotic patterns for some classes of groups.

math.GR↗

arXiv2025

Impact of the Pandemic on Currency Circulation in Brazil: Projections using the SARIMA Model

This study analyzes the impact of the COVID-19 pandemic on currency circulation in Brazil by comparing actual data from 2000 to 2023 with counterfactual projections using the \textbf{SARIMA(3,1,1)(3,1,4)\textsubscript{12}} model. The model was selected based on an extensive parameter search, balancing accuracy and simplicity, and validated through the metrics MAPE, RMSE, and AIC. The results indicate a significant deviation between projected and observed values, with an average difference of R\$ 47.57 billion (13.95\%). This suggests that the pandemic, emergency policies, and the introduction of \textit{Pix} had a substantial impact on currency circulation. The robustness of the SARIMA model was confirmed, effectively capturing historical trends and seasonality, though findings emphasize the importance of considering exogenous variables, such as interest rates and macroeconomic policies, in future analyses. Future research should explore multivariate models incorporating economic indicators, long-term analysis of post-pandemic currency circulation trends, and studies on public cash-holding behavior. The results reinforce the need for continuous monitoring and econometric modeling to support decision-making in uncertain economic contexts.

econ.GN↗