Symbolic solutions of some linear recurrences |
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| Authors: | E. Di Nardo D. Senato |
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| Affiliation: | Mathematics and Computer Science Department, University of Basilicata, Viale dell'Ateneo Lucano 10, 85100 Potenza, Italy |
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| Abstract: | A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a random variable with no reference to any probability space. We give several examples of applications and state an explicit form for the class of linear recurrences involving Sheffer sequences satisfying a special initial condition. The results here presented can be easily implemented in a symbolic software. |
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| Keywords: | Linear recurrences Sheffer sequences Classical umbral calculus Dyck paths |
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