New congruences for $$\ell $$ -regular partitions for $$\ell \in \{5,6,7,49\}$$

The Ramanujan Journal - Tập 40 - Trang 649-668 - 2016
Zakir Ahmed1, Nayandeep Deka Baruah1
1Department of Mathematical Sciences, Tezpur University, Sonitpur, India

Tóm tắt

We find several new congruences for $$\ell $$ -regular partitions for $$\ell \in \{5,6,7,49\}$$ and also find alternative proofs of the congruences for 10- and 20-regular partitions which were proved earlier by Carlson and Webb (Ramanujan J 33:329–337, 2014) by using the theory of modular forms. We use certain p-dissections of $$(q;q)_{\infty }$$ , $$\psi (q)$$ , $$(q;q)_{\infty }^3$$ and $$\psi (q^2)(q;q)_{\infty }^2$$ .

Tài liệu tham khảo

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