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.
@article{10_37236_11606,
author = {Liam Armstrong and Bryan Ducasse and Thomas Meyer and Holly Swisher},
title = {Generalized {Alder-type} partition inequalities},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11606},
zbl = {1516.05008},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11606/}
}
TY - JOUR
AU - Liam Armstrong
AU - Bryan Ducasse
AU - Thomas Meyer
AU - Holly Swisher
TI - Generalized Alder-type partition inequalities
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11606/
DO - 10.37236/11606
ID - 10_37236_11606
ER -
