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Title: Generalized Alder-Type Partition Inequalities
In 2020, Kang and Park conjectured a "level $$2$$" Alder-type partition inequality which encompasses the second Rogers-Ramanujan Identity. Duncan, Khunger, the fourth author, and Tamura proved Kang and Park's conjecture for all but finitely many cases utilizing a "shift" inequality and conjectured a further, weaker generalization that would extend both Alder's (now proven) as well as Kang and Park's conjecture to general level. Utilizing a modified shift inequality, Inagaki and Tamura have recently proven that the Kang and Park conjecture holds for level $$3$$ in all but finitely many cases. They further conjectured a stronger shift inequality which would imply a general level result for all but finitely many cases. Here, we prove their conjecture for large enough $$n$$, generalize the result for an arbitrary shift, and discuss the implications for Alder-type partition inequalities.  more » « less
Award ID(s):
2101906
PAR ID:
10441056
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
The Electronic Journal of Combinatorics
Date Published:
Journal Name:
The Electronic Journal of Combinatorics
Volume:
30
Issue:
2
ISSN:
1077-8926
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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