A bijection proof of Andrews-Merca integer partition theorem
| Title: | A bijection proof of Andrews-Merca integer partition theorem |
|---|---|
| Authors: | Liu, Ji-Cai |
| Publication Year: | 2024 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Combinatorics, Mathematics - Number Theory, 05A17, 05A19 |
| More Details: | Andrews and Merca [J. Combin. Theory Ser. A 203 (2024), Art. 105849] recently obtained two interesting results on the sum of the parts with the same parity in the partitions of $n$ (the modulo $2$ case), the proof of which relies on generating functions. Motivated by Andrews and Merca's results, we define six statistics related to the partitions of $n$ and show that the two triples of the six statistics are equidistributed. From this equidistributed result, we derive modulo $m$ extensions of Andrews and Merca's results for all integers $m\ge 2$. The proof of the main result is based on a general bijection on the set of partitions of $n$. Comment: The bijection constructed in this paper already exists in the known literature |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2405.00063 |
| Accession Number: | edsarx.2405.00063 |
| Database: | arXiv |
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