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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.56 no.2 Bogotá jul./dez. 2022 Epub 03-Fev-2024
https://doi.org/10.15446/recolma.v56n2.108370
Original articles
Palindromic and Colored Superdiagonal Compositions
Composiciones Superdiagonales Palíndromas y Coloreadas
1 Universidad Industrial de Santander, Bucaramanga, Colombia
2 Universidad Nacional de Colombia, Bogotá, Colombia
A superdiagonal composition is one in which the i-th part or summand is of size greater than or equal to i. In this paper, we study the number of palindromic superdiagonal compositions and colored superdiagonal compositions. In particular, we give generating functions and explicit combinatorial formulas involving binomial coefficients and Stirling numbers of the first kind.
Keywords: Compositions; palindromic compositions; colored compositions; generating functions; combinatorial identities
Una composición superdiagonal es aquella composición en la que la i-ésima parte (o sumando) tiene un tamaño mayor o igual que i. En este artículo, estudiamos el número de composiciones superdiagonales palindrómicas y composiciones superdiagonales coloreadas. En particular, damos funciones generatrices y fórmulas combinatorias explícitas que involucran coeficientes binomiales y números de Stirling de la primera clase.
Palabras clave: Composiciones; composiciones palíndromas; composiciones coloreadas; funciones generatrices; identidades combinatorias
References
1. J. R. Acosta, Y. Caicedo, J. P. Poveda, J. L. Ramírez, and M. Shattuck, Some new restricted n-color functions, J. Integer Seq. 22 (2019), no. Art. 19.6.4. [ Links ]
2. A. K. Agarwal, n-colour compositions, Indian J. Pure Appl. Math. 31 (2000), no. 11, 1421-1427. [ Links ]
3. J. J. Bravo, J. L. Herrera, J. L. Ramírez , and M. Shattuck , n-color palindromic compositions with restricted subscripts, Proc. Indian Acad. Sci. Math. Sci. 131 (2021), no. 9, 1-13. [ Links ]
4. A. Collins, C. Dedrickson, and H. Wang, Binary words, n-color compositions and bisection of the Fibonacci numbers, Fibonacci Quart. 51 (2013), no. 2, 130-136. [ Links ]
5. E. Deutsch, E. Munarini, and S. Rinaldi, Skew dyck paths, area, and superdiagonal bargraphs, J. Statist. Plann. Inference 140 (2010), 1550-1562. [ Links ]
6. Y. H. Guo, n-color odd self-inverse compositions, J. Integer Seq . 17 (2014), no. Art. 14.10.5. [ Links ]
7. S. Heubach and T. Mansour, Combinatorics of compositions and words, CRC Press, Boca Raton, FL, 2009. [ Links ]
8. V. E. Hoggatt and M. Bicknell, Palindromic compositions, Fibonacci Quart . 13 (1975), 350-356. [ Links ]
9. A. Munagi, Inverse-conjugate compositions modulo m, J. Comb. Math. Comb. Comput. 110 (2019), 249-257. [ Links ]
10. G. Narang and A. K. Agarwal, n-color self-inverse compositions, Proc. Indian Acad. Sci. Math . Sci. 116 (2006), no. 3, 257-266. [ Links ]
11. C. Shapcott, c-color compositions and palindromes, Fibonacci Quart . 50 (2012), no. 4, 297-303. [ Links ]
12. N. J. A. Sloane, The on-line encyclopedia of integer sequences, http://oeis.org. [ Links ]
Received: May 27, 2019; Accepted: October 16, 2022
This is an open-access article distributed under the terms of the Creative Commons Attribution License
