Runqiao Li
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View article: On the combinatorics of r-chain minimal and maximal excludants
On the combinatorics of r-chain minimal and maximal excludants Open
The minimal excludant (mex) of a partition was introduced by Grabner and Knopfmacher under the name `least gap' and was revived by a couple of papers due to Andrews and Newman. It has been widely studied in recent years together with the c…
View article: A NEW REFINEMENT OF FINE’S PARTITION THEOREM
A NEW REFINEMENT OF FINE’S PARTITION THEOREM Open
We find a new refinement of Fine’s partition theorem on partitions into distinct parts with the minimum part odd. As a consequence, we obtain two companion partition identities. Both analytic and combinatorial proofs are provided.
View article: GENERALISATION OF A RESULT ON DISTINCT PARTITIONS WITH BOUNDED PART DIFFERENCES
GENERALISATION OF A RESULT ON DISTINCT PARTITIONS WITH BOUNDED PART DIFFERENCES Open
We generalise a result of Chern [‘A curious identity and its applications to partitions with bounded part differences’, New Zealand J. Math. 47 (2017), 23–26] on distinct partitions with bounded difference between largest and smallest part…