Arithmetic properties for a partition function related to the Ramanujan/Watson mock theta function $$\omega (q)$$

Recently, Andrews, Dixit, and Yee introduced a new partition function \(p_{\omega }(n)\) that denotes the number of partitions of n in which each odd part is less than twice the smallest part. The generating function of \(p_{\omega }(n)\) is associated with the third-order mock theta function \(\omega (q)\). Andrews, Passary, Sellers, and Yee proved three infinite families of congruences modulo 4 and 8 for \(p_{\omega }(n)\) and provided elementary proofs of congruences modulo 5 for \(p_{\omega }(n)\) which were first discovered by Waldherr. In this paper, we prove some new congruences modulo 5 and powers of 2 for \(p_{\omega }(n)\). In particular, we obtain some non-standard congruences for \(p_{\omega }(n)\). For example, we prove that for \(k\ge 0\), \( p_{\omega }\left( \frac{7\times 5^{2k+1}+1 }{3}\right) \equiv (-1)^k \ (\mathrm{mod}\ 5) \) and \( p_\omega \left( \frac{2^{2k+7}+1}{3}\right) \equiv 1251 \times (-1)^k \ (\mathrm{mod}\ 2^{11})\).