Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  extend the Andrews-Olsson identity to two-colored partitions. Regarding the sets of proper Young walls of quantum affine algebras g n = A 2 n ( 2 ) , A 2 n - 1 ( 2 ) , B n ( 1 ) , D n ( 1 ) and D n + 1 ( 2 ) as the sets of two-colored partitions, the extended Andrews-Olsson identity implies that the generating functions of the sets of reduced Young walls have very simple formulae: ? i = 1 ∞ ( 1 + t i ) ? i where? ? i = 0 , 1 ?or?2,?and ? i ?varies?periodically. Moreover,  generalize Bessenrodt's algorithms to prove the extended Andrews-Olsson identity in an alternative way. From these algorithms,  can give crystal structures on certain subsets of pair of strict partitions which are isomorphic to the crystal bases B ( ? ) of the level 1 highest ight modules V ( ? ) over U q ( g n ) .
['Se-Jin Oh']
I am writing a research paper on a idea The Andrews-Olsson identity and Bessenrodt insertion algorithm on Young walls
[{"from": "human", "value": "I am writing a research paper on a idea The Andrews-Olsson identity and Bessenrodt insertion algorithm on Young walls"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  extend the Andrews-Olsson identity to two-colored partitions. Regarding the sets of proper Young walls of quantum affine algebras g n = A 2 n ( 2 ) , A 2 n - 1 ( 2 ) , B n ( 1 ) , D n ( 1 ) and D n + 1 ( 2 ) as the sets of two-colored partitions, the extended Andrews-Olsson identity implies that the generating functions of the sets of reduced Young walls have very simple formulae: ? i = 1 \u221e ( 1 + t i ) ? i where? ? i = 0 , 1 ?or?2,?and ? i ?varies?periodically. Moreover,  generalize Bessenrodt's algorithms to prove the extended Andrews-Olsson identity in an alternative way. From these algorithms,  can give crystal structures on certain subsets of pair of strict partitions which are isomorphic to the crystal bases B ( ? ) of the level 1 highest ight modules V ( ? ) over U q ( g n ) ."}]