Professor Saikia is interested in combinatorics broadly, which also includes some amount of number theory and theoretical computer science.
In combinatorics, he works on enumerating alternating sign matrices and plane partitions. The enumeration problems are typically solved using techniques emerging from a variety of fields, including statistical physics and representation theory. As an offshoot of this work, he is also interested in tiling problems and matching theory. In addition, he is very interested in integer partitions and understanding various partition statistics and exploring their combinatorial structures.
In number theory, he is interested in understanding the odd perfect number problem and exploring various generalized perfect numbers.
In theoretical computer science, he is interested in understanding combinatorial algorithms. Additionally, he is interested in finding algorithms to understand the arithmetic properties of different classes of integer partitions.