A latin square of order $n$ with pairwise disjoint subsquares of orders $h_1,\dots,h_k$ such that $h_1+\dots+h_k = n$ is known as a realization. The existence of realizations is a partially solved problem with a few general results for an arbitrary number of subsquares, $k$. Requiring only that $h_1+\dots+h_k\leq n$ gives a variation of the problem that has few known results. In this paper we prove a general necessary condition for existence and completely determine existence when there are at most three subsquares or the subsquares are all of the same order. Importantly, we prove that if $h_1\geq h_2\geq\dots\geq h_k$ and $n\geq h_1+\sum_{i=1}^kh_i$ then such a latin square always exists.
In 1782, Euler conjectured that no Latin square of order $n\equiv 2\; \textrm{mod}\; 4$ has a decomposition into transversals. While confirmed for $n=6$ by Tarry in 1900, Bose, Parker, and Shrikhande constructed counterexamples in 1960 for each $n\equiv 2\; \textrm{mod}\; 4$ with $n\geq 10$. We show that, in fact, counterexamples are extremely common, by showing that if a Latin square of order $n$ is chosen uniformly at random then with high probability it has a decomposition into transversals.
Javier Alonso Villegas Luis, Marco Antonio Sobrevilla Cabezudo
Linguistic features remain essential for interpretability and tasks that involve style, structure, and readability, but existing Spanish tools offer limited coverage. We present PUCP-Metrix, an open-source and comprehensive toolkit for linguistic analysis of Spanish texts. PUCP-Metrix includes 182 linguistic metrics spanning lexical diversity, syntactic and semantic complexity, cohesion, psycholinguistics, and readability. It enables fine-grained, interpretable text analysis. We evaluate its usefulness on Automated Readability Assessment and Machine-Generated Text Detection, showing competitive performance compared to an existing repository and strong neural baselines. PUCP-Metrix offers a comprehensive and extensible resource for Spanish, supporting diverse NLP applications.
This study presents an LLM-assisted annotation pipeline for the sociolinguistic and topical analysis of bilingual discourse in two typologically distinct contexts: Spanish-English and Spanish-Guaraní. Using large language models, we automatically labeled topic, genre, and discourse-pragmatic functions across a total of 3,691 code-switched sentences, integrated demographic metadata from the Miami Bilingual Corpus, and enriched the Spanish-Guaraní dataset with new topic annotations. The resulting distributions reveal systematic links between gender, language dominance, and discourse function in the Miami data, and a clear diglossic division between formal Guaraní and informal Spanish in Paraguayan texts. These findings replicate and extend earlier interactional and sociolinguistic observations with corpus-scale quantitative evidence. The study demonstrates that large language models can reliably recover interpretable sociolinguistic patterns traditionally accessible only through manual annotation, advancing computational methods for cross-linguistic and low-resource bilingual research.
Jaime E. Cuellar, Oscar Moreno-Martinez, Paula Sofia Torres-Rodriguez
et al.
One fundamental question for the social sciences today is: how much can we trust highly complex predictive models like ChatGPT? This study tests the hypothesis that subtle changes in the structure of prompts do not produce significant variations in the classification results of sentiment polarity analysis generated by the Large Language Model GPT-4o mini. Using a dataset of 100.000 comments in Spanish on four Latin American presidents, the model classified the comments as positive, negative, or neutral on 10 occasions, varying the prompts slightly each time. The experimental methodology included exploratory and confirmatory analyses to identify significant discrepancies among classifications. The results reveal that even minor modifications to prompts such as lexical, syntactic, or modal changes, or even their lack of structure impact the classifications. In certain cases, the model produced inconsistent responses, such as mixing categories, providing unsolicited explanations, or using languages other than Spanish. Statistical analysis using Chi-square tests confirmed significant differences in most comparisons between prompts, except in one case where linguistic structures were highly similar. These findings challenge the robustness and trust of Large Language Models for classification tasks, highlighting their vulnerability to variations in instructions. Moreover, it was evident that the lack of structured grammar in prompts increases the frequency of hallucinations. The discussion underscores that trust in Large Language Models is based not only on technical performance but also on the social and institutional relationships underpinning their use.
Jose Jeffs Munizaga, Pablo Lacoste, Juan Carlos Skewes
et al.
Se examina la valoración de la yerba mate como patrimonio agroalimentario regional, en el proceso de construcción del ideario americanista durante la gestión de Juan Manuel de Rosas al frente de la Confederación Argentina. Se detecta que la cultura de la yerba mate alcanzó un fuerte arraigo en la sociedad del Cono Sur en los siglos XVII y XVIII, pero, después de la independencia, la estrategia comercial británica procuró sustituirla por el té, producto imperial funcional a sus intereses. Este proyecto tuvo éxito en varios territorios, como por ejemplo en Chile, donde la élite se plegó a la moda impuesta por los ingleses. Pero en el Río de la Plata, Rosas se empeñó en promover y fortalecer la cultura del mate, como medio estratégico de afirmar la identidad americanista y de resistencia a las pretensiones neocoloniales europeas. Con esta actitud, Rosas fue un pionero en la valoración del patrimonio agroalimentario regional.
We show that the sets of $d$-dimensional Latin hypercubes over a non-empty set $X$, with $d$ running over the positive integers, determine an operad which is isomorphic to a sub-operad of the endomorphism operad of $X$. We generalise this to categories with finite products, and then further to internal versions for certain Cartesian closed monoidal categories with pullbacks.
Existing Latin treebanks draw from Latin's long written tradition, spanning 17 centuries and a variety of cultures. Recent efforts have begun to harmonize these treebanks' annotations to better train and evaluate morphological taggers. However, the heterogeneity of these treebanks must be carefully considered to build effective and reliable data. In this work, we review existing Latin treebanks to identify the texts they draw from, identify their overlap, and document their coverage across time and genre. We additionally design automated conversions of their morphological feature annotations into the conventions of standard Latin grammar. From this, we build new time-period data splits that draw from the existing treebanks which we use to perform a broad cross-time analysis for POS and morphological feature tagging. We find that BERT-based taggers outperform existing taggers while also being more robust to cross-domain shifts.
O livro Der moderne Denkmalkultus, sein Wesen und seine Entsehung (O culto moderno dos monumentos: sua essência e sua gênese), do historiador da arte Alois Riegl (1858-1905), é hoje considerado uma das obras capitais do diálogo que chamamos de Teorias da Conservação e Restauro, e no Brasil estudado cada vez mais, com concepções inéditas e mesmo pioneiras em 1903, quando foi publicado. A leitura mais atenta do conjunto da obra de Riegl revela uma construção muito mais sofisticada do que aparece à leitura isolada do Denkmalkultus, como usual na área do Patrimônio. Em seus livros, Riegl explora e estabelece uma concepção particular de história e do ofício do historiador. Nela, diacronicamente, estão presentes a ênfase crescente da História como um devir contínuo, onde eram reconhecíveis linhas de sentido de longo prazo – como os vetores progressivos e reativos coexistentes
em cada obra de arte –, e a possibilidade de épocas diferentes se tangenciarem, a partir do olhar para o passado, inclusive do historiador contemporâneo. Também se encontram, sincronicamente, as contribuições da História Cultural e o estudo das cosmovisões. Revela-se
assim que o Denkmalkultus, como outros textos de Riegl, não era apenas uma descrição dos processos globais que acreditava existir desde o Paleolítico até a Era Moderna, como um exemplo concreto da progressão teleológica, essencial para interpretar sua obra.
Isabel Flores de Oliva (1586–1617), generally known as Saint Rose of Mary or Saint Rose of Lima, became the first and, until today, the most venerated Catholic saint of Latin America. Almost immediately after her death, this Dominican of the Third Order, who died young and won fame for her highly ascetic life, various virtues and immovable faith, developed a cult following in Peru. Soon enough the cult had spread across South America and Europe. The topic of Saint Rose of Lima has been addressed in a great many publications that appeared in various (primarily Spanish-speaking) countries, but in Lithuania, the devotion to and images of this saint have not received specific research attention. By referring to the published sources and manuscripts, as well as the surviving ecclesiastical artworks, the author of this paper aims to discuss in more detail how information about the life and personality of Saint Rose of Lima was disseminated in the Grand Duchy of Lithuania, what information about Latin America, its culture and people was conveyed in these sources, whether it was reflected in the icono- graphy of the saint, and if so, how.
It is well known that, within the Latin production of written text, peculiar metric schemes were followed not only in poetic compositions, but also in many prose works. Such metric patterns were based on so-called syllabic quantity, i.e., on the length of the involved syllables, and there is substantial evidence suggesting that certain authors had a preference for certain metric patterns over others. In this research we investigate the possibility to employ syllabic quantity as a base for deriving rhythmic features for the task of computational authorship attribution of Latin prose texts. We test the impact of these features on the authorship attribution task when combined with other topic-agnostic features. Our experiments, carried out on three different datasets, using two different machine learning methods, show that rhythmic features based on syllabic quantity are beneficial in discriminating among Latin prose authors.
This article reconstructs the life and trajectory of Juan Carlos Colombres or Landrú and his relantionship with the magazine Tía Vicenta, one of his creations. In this way, the life story of Colombres will be intertwined with the historical context that surrounded it. In turn, relations with other comedians and cartoonists of the time as well as politicians and military on duty will be presented.
Latin America. Spanish America, French literature - Italian literature - Spanish literature - Portuguese literature
Jacob W. Cooper, Daniel Kral, Ander Lamaison
et al.
We prove a conjecture by Garbe et al. [arXiv:2010.07854] by showing that a Latin square is quasirandom if and only if the density of every 2x3 pattern is 1/720+o(1). This result is the best possible in the sense that 2x3 cannot be replaced with 2x2 or 1xN for any N.
We introduce a notion of parity for transversals, and use it to show that in Latin squares of order $2 \bmod 4$, the number of transversals is a multiple of 4. We also demonstrate a number of relationships (mostly congruences modulo 4) involving $E_1,\dots, E_n$, where $E_i$ is the number of diagonals of a given Latin square that contain exactly $i$ different symbols. Let $A(i\mid j)$ denote the matrix obtained by deleting row $i$ and column $j$ from a parent matrix $A$. Define $t_{ij}$ to be the number of transversals in $L(i\mid j)$, for some fixed Latin square $L$. We show that $t_{ab}\equiv t_{cd}\bmod2$ for all $a,b,c,d$ and $L$. Also, if $L$ has odd order then the number of transversals of $L$ equals $t_{ab}$ mod 2. We conjecture that $t_{ac} + t_{bc} + t_{ad} + t_{bd} \equiv 0 \bmod 4$ for all $a,b,c,d$. In the course of our investigations we prove several results that could be of interest in other contexts. For example, we show that the number of perfect matchings in a $k$-regular bipartite graph on $2n$ vertices is divisible by $4$ when $n$ is odd and $k\equiv0\bmod 4$. We also show that $${\rm per}\, A(a \mid c)+{\rm per}\, A(b \mid c)+{\rm per}\, A(a \mid d)+{\rm per}\, A(b \mid d) \equiv 0 \bmod 4$$ for all $a,b,c,d$, when $A$ is an integer matrix of odd order with all row and columns sums equal to $k\equiv2\bmod4$.
This paper will present some intuitive interpretation of the parastrophe transformations of arbitrary Latin square. With this trick, we can generate the parastrophes of arbitrary Latin square directly from the original one without generating the orthogonal array. The relations of isotopisms and parastrophe transformations in composition will also be shown. It will solve the problem that when F1*I1=I2*F2 how can we obtain I2 and F2 from I1 and F1, where I1 and I2 are isotopisms while F1 and F2 are parastrophe transformations and "{*}" is the composition of transformations. These methods could distinctly simplify the computation on a computer for the issues related to main classes of Latin squares. This will improve the efficiency apparently in computation for some related problems.
We are seeking a sufficient condition that forces a transversal in a generalized Latin square. A generalized Latin square of order $n$ is equivalent to a proper edge-coloring of $K_{n,n}$. A transversal corresponds to a multicolored perfect matching. Akbari and Alipour defined $l(n)$ as the least integer such that every properly edge-colored $K_{n,n}$, which contains at least $l(n)$ different colors, admits a multicolored perfect matching. They conjectured that $l(n)\leq n^2/2$ if $n$ is large enough. In this note we prove that $l(n)$ is bounded from above by $0.75n^2$ if $n>1$. We point out a connection to anti-Ramsey problems. We propose a conjecture related to a well-known result by Woolbright and Fu, that every proper edge-coloring of $K_{2n}$ admits a multicolored $1$-factor.
Este artigo pretende fazer uma análise, de caráter historiográfico, com intuito de compreender a dinâmica na prática historiográfica no período que permeou o entorno das décadas de 1960 a 1980, observando em que medida algumas linhas de pesquisa possuem ou não paralelo, como é o caso micro-história italiana e da descontinuidade presente na obra de Michel Foucault, francês. O título deste trabalho surgiu de duas disciplinas do doutorado que permitiram vislumbrar certo paralelismo entre as propostas, mas que ao fim, como poderá ser constatado, não se mostrou totalmente coerente. Assim, o título serve de leitmotiv para o texto, mas não expressa o resultado da investigação.