In a recent paper of Andrews and Paule, several Schmidt-type partition identities are considered within the framework of MacMahon's Partition Analysis. Following their work, we derive a new Schmidt-type identity concerning diagonal hooks of partitions. We provide an analytic proof based on MacMahon's Partition Analysis and a combinatorial proof through an involution on the set of partitions. We also establish connections between Schmidt-type distinct partitions and partitions with nonpositive and negative cranks.
@article{10_37236_10803,
author = {Shane Chern and Ae Ja Yee},
title = {Diagonal hooks and a {Schmidt-type} partition identity},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {2},
doi = {10.37236/10803},
zbl = {1492.11146},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10803/}
}
TY - JOUR
AU - Shane Chern
AU - Ae Ja Yee
TI - Diagonal hooks and a Schmidt-type partition identity
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/10803/
DO - 10.37236/10803
ID - 10_37236_10803
ER -
%0 Journal Article
%A Shane Chern
%A Ae Ja Yee
%T Diagonal hooks and a Schmidt-type partition identity
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/10803/
%R 10.37236/10803
%F 10_37236_10803
Shane Chern; Ae Ja Yee. Diagonal hooks and a Schmidt-type partition identity. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10803
