Proof of a Lin-Peng-Toh's conjecture on an Andrews-Beck type congruence |
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Institution: | School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou, 215009, Jiangsu Province, PR China |
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Abstract: | Recently, Andrews proved two conjectures of Beck related to ranks of partitions. Very recently, Chern established some results on weighted rank and crank moments and proved many Andrews-Beck type congruences. Motivated by Andrews and Chern's work, Lin, Peng and Toh proved a number of Andrews-Beck type congruences for k-colored partitions. At the end of their paper, Lin, Peng and Toh posed several conjectures on Andrews-Beck type congruences. In this paper, we confirm one of those conjectures based on some q-series identities. |
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Keywords: | Partitions Rank Crank Andrews-Beck type congruences |
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