A family of Bell transformations
| Autor: | Juan B. Gil, Daniel Birmajer, Michael D. Weiner |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Sequence Mathematics - Number Theory Probability (math.PR) 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Convolution of probability distributions 01 natural sciences Enumerative combinatorics Theoretical Computer Science Bell polynomials Range (mathematics) 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Inverse relation Combinatorics (math.CO) Number Theory (math.NT) Variety (universal algebra) Algebraic number Mathematics - Probability Mathematics |
| DOI: | 10.48550/arxiv.1803.07727 |
| Popis: | We introduce a family of sequence transformations, defined via partial Bell polynomials, that may be used for a systematic study of a wide variety of problems in enumerative combinatorics. This family includes some of the transformations listed in the paper by Bernstein & Sloane, now seen as transformations under the umbrella of partial Bell polynomials. Our goal is to describe these transformations from the algebraic and combinatorial points of view. We provide functional equations satisfied by the generating functions, derive inverse relations, and give a convolution formula. While the full range of applications remains unexplored, in this paper we show a glimpse of the versatility of Bell transformations by discussing the enumeration of several combinatorial configurations, including rational Dyck paths, rooted planar maps, and certain classes of permutations. 22 pages. Final version that includes referee's comments |
| Databáze: | OpenAIRE |
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