Geodesic
A generalization of partition identities for first differences of partitions of \(n\) into at most \(m\) parts
Acadia Larsen1
1University of Texas: Rio Grande Valley
The electronic journal of combinatorics, Tome 28 (2021) no. 3
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We show for a prime power number of parts $m$ that the first differences of partitions into at most $m$ parts can be expressed as a non-negative linear combination of partitions into at most $m-1$ parts. To show this relationship, we combine a quasipolynomial construction of $p(n,m)$ with a new partition identity for a finite number of parts. We prove these results by providing combinatorial interpretations of the quasipolynomial of $p(n,m)$ and the new partition identity. We extend these results by establishing conditions for when partitions of $n$ with parts coming from a finite set $A$ can be expressed as a non-negative linear combination of partitions with parts coming from a finite set $B$.
DOI : 10.37236/8199
Classification : 11P84, 05A17, 05A19
Mots-clés : partitions, linear combinations of partitions

Acadia Larsen  1

1 University of Texas: Rio Grande Valley 
@article{10_37236_8199,
     author = {Acadia Larsen},
     title = {A generalization of partition identities for first differences of partitions of \(n\) into at most \(m\) parts},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {3},
     doi = {10.37236/8199},
     zbl = {1477.11180},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8199/}
}
TY  - JOUR
AU  - Acadia Larsen
TI  - A generalization of partition identities for first differences of partitions of \(n\) into at most \(m\) parts
JO  - The electronic journal of combinatorics
PY  - 2021
VL  - 28
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/8199/
DO  - 10.37236/8199
ID  - 10_37236_8199
ER  - 
%0 Journal Article
%A Acadia Larsen
%T A generalization of partition identities for first differences of partitions of \(n\) into at most \(m\) parts
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8199/
%R 10.37236/8199
%F 10_37236_8199
Acadia Larsen. A generalization of partition identities for first differences of partitions of \(n\) into at most \(m\) parts. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/8199

Cité par Sources :