Abstract
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.
| Language | English (US) |
|---|---|
| Pages | 38-54 |
| Number of pages | 17 |
| Journal | Discrete Mathematics |
| Volume | 342 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2019 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
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A family of Bell transformations. / Birmajer, Daniel; Gil, Juan Bautista; Weiner, Michael David.
In: Discrete Mathematics, Vol. 342, No. 1, 01.01.2019, p. 38-54.Research output: Contribution to journal › Article
TY - JOUR
T1 - A family of Bell transformations
AU - Birmajer, Daniel
AU - Gil, Juan Bautista
AU - Weiner, Michael David
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85054466717&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85054466717&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2018.09.011
DO - 10.1016/j.disc.2018.09.011
M3 - Article
VL - 342
SP - 38
EP - 54
JO - Discrete Mathematics
T2 - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 1
ER -