2024/04/27 by Liu, Ji-Cai
#05A17 #05A19 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2405.00063
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≥ 2. The proof of the main result is based on a general bijection on the set of partitions of n.