Witness identities for three Ramanujan congruences

Nayandeep Deka Baruah, Hirakjyoti Das, Abhishek Sarma

For the unrestricted partition function $p(n)$ for integers $n\ge 0$, it is known that $p(49n+19)\equiv 0(\mathrm{mod}49)$, $p(49n+33)\equiv 0(\mathrm{mod}49)$, and $p(49n + 40) \equiv…