Legendre theorems for certain overpartitions and overpartition pairs
George E. Andrews, Mohamed El Bachraoui
TL;DR
This paper extends Legendre-type formulas to overpartition pairs, establishing new identities and equalities among subclasses of overpartitions and overpartition pairs, thus broadening the theoretical understanding of these combinatorial objects.
Contribution
It introduces new Legendre theorems for overpartition pairs, complementing existing formulas for overpartitions and establishing novel equalities.
Findings
Derived new Legendre theorems for overpartition pairs
Established equalities among subclasses of overpartitions and overpartition pairs
Extended classical formulas to more complex combinatorial structures
Abstract
Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subclasses of overpartitions and overpartition pairs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsadvanced mathematical theories