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In this paper we extend the results of Getu [2] on evaluating determinants via generating functions to a broader class of matrices, which contain convolution matrices. As an immediate application of our new findings, we develop the method of finding the determinant representation of a well-known sequence. By creating the determinant representations of Chebyshev polynomials of the first kind and Stirling numbers of the second kind, we illustrate the idea of the method.

Yupana is the name given to the counting deviceor abacusof the Incas; in the indigenous Andean language of Quechua, "yupay" means "to count." Counting was a fundamental aspect of structuring such an extensive and elaborate civilization as that of the Incas, which reached its height in the fifteenth and sixteenth centuries with an estimated population in the millions and extending across the diverse climatic regions of northern Chile and Argentina, Ecuador, Bolivia, Peru, and the southern part of Colombia. This calculating device along with its corresponding recording devicethe quipuwere the main technologies that organized the Inca population and controlled the distribution of goods and labor responsibilities. While the quipu knot records were static registries of amounts calculated and served as the authoritative voice of quantities paid, quantities due, and standard measurements and statistics, the yupana would have been the device used to calculate (but not register) those amounts later tied into quipu cords. While the knot structure of the quipu was not suitable for the manipulation of numbers nor performing repeated algorithms, the yupana is a table upon which counters (of beans, corn, pebbles, grains, or other tokens) can be freely moved, thus facilitating the execution of distinct numeric operations. *

En este trabajo los autores buscan rescatar la memoria histórica de unas matemáticas olvidadas: las que estructuraron el terreno andino antes de la llegada de los conquistadores españoles en el siglo XVI. Las tradiciones numéricas de las culturas autóctonas andinas han sido negadas, borradas, y apropiadas por discursos coloniales y extranjeros que han interpretado el pasado andino de acuerdo a sus propios términos negando la existencia de otras formas de conocimiento incluyendo las de sus propios creadores. Trazar estos procesos históricos globales permite recuperar la memoria histórica andina, la cual se podría incorporar a clases de etnomatemáticas en un futuro. Lograr difundir la historia intelectual y matemática del pasado andino tiene la potencia de re-ubicar el pensamiento indígena dentro de las estructuras unilaterales de poder, así cambiando la forma en que la agencia indígena se reconoce y promoviendo la pluralidad enriquecedora de nuestra sociedad. Palabras Clave: Quipu; Memoria histórica; Teorías de-coloniales; Matemáticas andinas.

This issue of the Revista Latinoamericana de Etnomatemática (RLE, Latin American Journal of Ethnomathematics) serves as evidence of the extensive work carried out by researchers around the globe that contributes to the continually growing field of Ethnomathematics and its applications. While Ethnomathematics has a long tradition of scholarship and presence within Latin America, this shared endeavor is a dynamic and diverse effort constantly informed by conversations with the community of practice at large. In this way, we can consider this publication a snapshot of the connections, conversations, efforts, and initiatives that our membership and readership continually maintain, across many language, disciplinary, and institutional divides. This issue is also indicative of the diversity of Ethnomathematics. The featured contributions represent all languages (Spanish, Portuguese, and English) and genres (articles of investigation, reflections, literary reviews, and interviews) currently supported by the journal. The contributing authors have positioned their work in relation to a wide range of geographic contexts (including Chile, Argentina, Colombia, Brazil, Mexico, Paraguay, Papua New Guinea, Panama, Costa Rica, Nicaragua, Guatemala, and the United States), demographics (Mapuche, Arhuaco, Kanamari, Mixtec, Guarani-Ñandeva, community leaders, students, low-income populations, teachers, women artisans, farmers, researchers), and pedagogical settings (indigenous schools, elementary schools, high schools, one-room schools, the workplace, the home, the community) and have employed diverse methodologies and theoretical frameworks in their research design and conclusions.

In this article I explore the benefits and dangers of intercultural contact in the context of the creation and diffusion of Chilam Balam books, sacred texts compiled mainly during the colonial period and used by Maya communities of Yucatan. I present the results of my fieldwork to the area which include the narrative of the disappearance and recreation of an unpublished Chilam Balam as well as a partial reproduction of its contents including a chapter on Maya Numbers and a collection of Maya hieroglyphs. This reproduction of an original unpublished Chilam Balam manuscript is a unique contribution to the field of Maya studies and evidence of the Maya episteme regarding numbers, time, and the universe.

RESUMO Neste artigo, eu exploro os benefícios e os perigos do contato intercultural no contexto da criação e da difusão dos livros Chilam Balam, que são textos sagrados que foram compilados, principalmente, durante o período colonial e utilizados por comunidades maias de Yucatan. Apresento os resultados de meu trabalho de campo nessa área que inclui a narrativa do desaparecimento e da re-criação de um Chilam Balam inédito, bem como uma reprodução parcial de seu conteúdo, incluindo um capítulo sobre os Números Maias e uma coleção de hieróglifos maias. Essa reprodução do manuscrito original inédito de Chilam Balam é uma contribuição única para o campo dos estudos maias e evidencia a episteme maia com relação aos números, ao tempo e ao universo.

RESUMEN En este artículo se exploran los beneficios y peligros del contacto intercultural en el contexto de la creación y la difusión de los libros del Chilam Balam, textos sagrados compilados principalmente durante el período colonial y utilizados por las comunidades mayas de Yucatán. Se presentan los resultados de mi trabajo de campo a la zona, que incluyen la narración de la desaparición y la re-creación de un Chilam Balam inédito, así como la reproducción parcial de su contenido incluyendo el capítulo de Números Mayas y una colección de los jeroglíficos mayas. Esta reproducción de un manuscrito inédito original del Chilam Balam es una contribución