Conteo de letras de una frase con los dedos y matrices
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jun 14, 2024
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https://doi.org/10.30878/ces.v31n0a19
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Fernando Ricardo González Díaz
http://orcid.org/0009-0009-9704-1119
Ricardo García Salcedo
http://orcid.org/0000-0003-0173-5466
http://orcid.org/0009-0009-9704-1119
Ricardo García Salcedo
http://orcid.org/0000-0003-0173-5466
Resumen
Se presenta un enfoque novedoso para contar letras en palabras o frases en español usando los dedos de la mano derecha. Con este fin, se utiliza un modelo algebraico basado en matrices para representar el conteo, el cual asegura que cada dedo y letra estén relacionados. Se demuestra que el conteo se repite una o cinco veces sin dejar dedos o letras sin asociar. Aunado a esto, se introduce la matriz de letras como una representación asociada al conteo y se establece que forma un monoide. Este estudio profundiza en el conteo de letras y su relación con las matrices con implicaciones en lingüística, criptografía y ciencias de la computación.
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Como citar
GONZÁLEZ DÍAZ, Fernando Ricardo; GARCÍA SALCEDO, Ricardo.
Conteo de letras de una frase con los dedos y matrices.
CIENCIA ergo-sum, [S.l.], v. 31, jun. 2024.
ISSN 2395-8782.
Disponible en: <https://cienciaergosum.uaemex.mx/article/view/20935>. Fecha de acceso: 12 oct. 2024
doi: https://doi.org/10.30878/ces.v31n0a19.
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Ciencias exactas y aplicadas
Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial-SinObrasDerivadas 4.0.
Citas
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Sabando Álvarez, M. C. (2020). Numerical monoids, numerical operads and applications to combinatorics (Bachelor’s thesis, Universidad de Investigación de Tecnología Experimental Yachay).
Soylu, F., Lester Jr, F. K., & Newman, S. D. (2018). You can count on your fingers: The role of fingers in early mathematical development. Journal of Numerical Cognition, 4(1), 107-135. https://doi.org/10.5964/jnc.v4i1.85
Steinberg, B. (2016). Representation theory of finite monoids. Springer.
Sylvester, J. J. (2009). XXXVII. On the relation between the minor determinants of linearly equivalent quadratic functions. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1(4), 295-305. https://doi.org/10.1080/14786445108646735
Weisstein, E. W. (2023). Right-Hand Rule. MathWorld. https://mathworld.wolfram.com/Right-HandRule.html
Ycart, B. (2012). Letter counting: astem cell for Cryptology, Quantitative Linguistics, and Statistics. https://arxiv.org/abs/1211.6847
Balari, S. (2014). Teoría de lenguajes formales: una introducción para lingüistas. https://ddd.uab.cat/record/116304>
Birchenall, L. B. y Müller, O. (2014). La teoría lingüística de Noam Chomsky: del inicio a la actualidad. Lenguaje, 42(2), 417-442.
Bender, A., & Beller, S. (2012). Nature and culture of finger counting: Diversity and representational effects of an embodied cognitive tool. Cognition, 124(2), 156-182.
Book, R. V., & Otto, F. (1993). String-rewriting systems. In R. V. Book & F. Otto, String-rewriting systems (pp. 35-64). New York: Springer Verlag.
Butterworth, B. (1999). What counts: How every brain is hardwired for math. Free Press.
Cayley, A. (2009). The collected mathematical papers. Cambridge: Cambridge University Press.
Ceballos, H. A. Z. y De Armas, T. R. A. (2013). Redefinición de grupos y subgrupo difusos. Scientia Et Technica, 18(2), 363-368.
Chomsky, N. (1970). Aspectos de la teoría de la sintaxis. Madrid: Aguilar.
Chomsky, N. (1978). Estructuras sintácticas. México: Siglo XXI.
Cohen, D. E. (1993). String rewriting — A survey for group theorists. In Graham A. Niblo & Martin A. Roller, Geometric Group Theory 1, 37-47.
Dehn, M. (1911). Über unendliche diskontinuierliche Gruppen. Mathematische Annalen, 71(1), 116-144. https://doi.org/10.1007/BF01456932
DeRocher, J. E., Miron, M. S., Patten, S. M., & Pratt, C. C. (1973). The counting of words: A review of the history, techniques and theory of word counts with annotated bibliography. New York: Syracuse University Research Corporation.
Domahs, F., Moeller, K., Huber, S., Willmes, K., & Nuerk, H. C. (2010). Embodied numerosity: implicit hand-based representations influence symbolic number processing across cultures. Cognition, 116(2), 251-266. http://doi.org/10.1016/j.cognition.2010.05.007
Gao, Z., MacFie, A., & Panario, D. (2011). Counting Words by Number of Occurrences of Some Patterns. The Electronic Journal of Combinatorics, 18(1).
Garay, C. E. (2019). Monoides abelianos en álgebra y geometría. México: CIMAT. http://personal.cimat.mx:8181/~cristhian.garay/escuela.pdf
Gavin, M. (2020). Is there a text in my data?(Part 1): On counting words. Journal of Cultural Analytics, 5(1).
Gelman, R., & Butterworth, B. (2005). Number and language: how are they related?. Trends in Cognitive Sciences, 9(1), 6-10.
Ghadbane, N. (2022). On public key cryptosystem based on the word problem in a group. Journal of Discrete Mathematical Sciences and Cryptography, 25(6), 1563-1568.
Grossman, S. I. (1994). Elementary linear algebra. USA: Cole Publishing Company Pacific Grove.
Ifranh, G. (1987). Las cifras: historia de una gran invención. Madrid: Alianza.
Jacobson, N. (2009). Basic Algebra I (second edition). New York: Dover Publications.
Jonsson, D. (2019). Magnitudes Reborn: Quantity Spaces as Scalable Monoids. Rings and Algebras. https://arxiv.org/abs/1911.07236
Lang, S. (2005). Undergraduate Algebra (3rd ed.). Berlin: Springer-Verlag.
Lasnik, H., & Lohndal, T. (2010). Government–binding/principles and parameters theory. WIREs. Wiley Interdisciplinary Reviews. Cognitive Science, 1(1), 40-50.
Liaqat, I., & Younas, W. (2021). Some important applications of semigroups. Journal of Mathematical Sciences & Computational Mathematics, 2(2), 317-321.
Lluis-Puebla, E. (2015). Teorías matemáticas, matemática aplicada y computación. CIENCIA ergo-sum, 13(1), 91-98. https://cienciaergosum.uaemex.mx/article/view/7894
Lothaire, M. (2005). Applied combinatorics on words. Cambridge University Press. https://doi.org/10.1017/CBO9781107341005
Luzardo, D., & Peña, A. J. (2006). Historia del álgebra lineal hasta los albores del siglo XX. Divulgaciones Matemáticas, 14(2), 153-170.
Maclellan, E. (1995). Counting all, counting on, counting up, counting down: The role of counting in learning to add and subtract. Education 3-13, 23(3), 17-21.
Previtali, P., Rinaldi, L., & Girelli, L. (2011). Nature or nurture in finger counting: a review on the determinants of the direction of number–finger mapping. Frontiers in Psychology, 2, 363.
Rosales, A. (2008). Evolución histórica del concepto de matriz. Mathematics, Education and Internet Journal, 9(1), 1-20. https://doi.org/10.18845/rdmei.v9i1.2038
Sabando Álvarez, M. C. (2020). Numerical monoids, numerical operads and applications to combinatorics (Bachelor’s thesis, Universidad de Investigación de Tecnología Experimental Yachay).
Soylu, F., Lester Jr, F. K., & Newman, S. D. (2018). You can count on your fingers: The role of fingers in early mathematical development. Journal of Numerical Cognition, 4(1), 107-135. https://doi.org/10.5964/jnc.v4i1.85
Steinberg, B. (2016). Representation theory of finite monoids. Springer.
Sylvester, J. J. (2009). XXXVII. On the relation between the minor determinants of linearly equivalent quadratic functions. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1(4), 295-305. https://doi.org/10.1080/14786445108646735
Weisstein, E. W. (2023). Right-Hand Rule. MathWorld. https://mathworld.wolfram.com/Right-HandRule.html
Ycart, B. (2012). Letter counting: astem cell for Cryptology, Quantitative Linguistics, and Statistics. https://arxiv.org/abs/1211.6847