Linear recurrence sequences and their convolutions via bell polynomials

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a basis of se- quences that can be obtained as the INVERT transform of the coefficients of the given recurrence relation. For such a basis sequence with generating function Y (t), and for any positive integer r, we give a formula for the convolved sequence generated by Y (t)r and prove that it satisfies an elegant recurrence relation.

Original languageEnglish (US)
JournalJournal of Integer Sequences
Volume18
Issue number1
StatePublished - 2014

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Bell Polynomials
Linear Recurrence
Convolution
Recurrence relation
Combinatorial Identities
Coefficient
Generating Function
Transform
Partial
Integer

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

Cite this

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title = "Linear recurrence sequences and their convolutions via bell polynomials",
abstract = "We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a basis of se- quences that can be obtained as the INVERT transform of the coefficients of the given recurrence relation. For such a basis sequence with generating function Y (t), and for any positive integer r, we give a formula for the convolved sequence generated by Y (t)r and prove that it satisfies an elegant recurrence relation.",
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journal = "Journal of Integer Sequences",
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Linear recurrence sequences and their convolutions via bell polynomials. / Birmajer, Daniel; Gil, Juan Bautista; Weiner, Michael David.

In: Journal of Integer Sequences, Vol. 18, No. 1, 2014.

Research output: Contribution to journalArticle

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AU - Gil, Juan Bautista

AU - Weiner, Michael David

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AB - We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a basis of se- quences that can be obtained as the INVERT transform of the coefficients of the given recurrence relation. For such a basis sequence with generating function Y (t), and for any positive integer r, we give a formula for the convolved sequence generated by Y (t)r and prove that it satisfies an elegant recurrence relation.

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