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I am a Research Associate 1 with Prof. Sunil Chandran in the Department of Computer Science and Automation at IISc Bangalore. I am interested in questions arising from Enumerative and Extremal Combinatorics. I have recently taken an interest in some aspects of Computational Complexity and Theoretical Computer Science.
I completed my BS-MS (Dual) Degree programme with a major in Mathematics from IISER Thiruvanthapuram in 2019. I defended my PhD thesis titled 'Polynomials arising in Permutation Enumeration' under the supervision of Prof. Krishnan Sivasubramanian from IIT Bombay in 2026.
Graph Theory at IISc
At IISc Bangalore, I have started studying the computation complexity of cube representations of trees. We believe that finding the minimum dimension on which trees can be represented as the intersection graphs of unit hypercubes is NP-hard. We are studying allied variants of this problem both from a computational complexity as well as from an upper bound point of view.
Extremal Combinatorics at IITB
I was also involved in the Extremal Combinatorics group headed by Niranjan Balachandran at IIT Bombay. Here, we initiated the study of path representations of graphs. A path representation of a graph G is a graph H whose edges can be partitioned into paths such that the vertex intersection graph of the paths is G. The path representation number of G is the minimum number of vertices that can host a graph H that is a path representation of G. We gave lower and upper bounds for the path representation number in terms of known graph parameters. We also outlined its connections to IC routing and neuroscience. We also gave an algorithmic scheme to find the path representation number of trees in polynomial time. We conjecture that planar graphs admit optimal planar representators.
Enumerative Combinatorics at IITB
At IIT Bombay, I started working on algebraic properties of polynomials arising in Enumerative Combinatorics. We studied gamma-positivity, log-concavity and real rootedness of polynomials that came up in permutation enumeration. I was able to prove the polynomials that enumerated descents and excedances over the even permutations had ultra-log-concave coefficients. It is conjectured that these polynomials have only real roots. I was also able to give a criterion that certifies log-concavity of combinatorial sequences that satisfy triangular recurrences. This criterion gives a unified approach to log-concavity of many sequences that appear in combinatorics such as the Eulerian numbers, Stirling numbers and Lah numbers.
Later on in my study at IIT Bombay, I took to studying the pattern avoidance in permutations. We were able to reformulate some recent results of Burstein, Kitaev, Han and Zhang in the language of sums of labelled posets which allowed us to ask more questions from a poset perspective. We were able to completely classify the shape-Wilf equivalence of poset patterns of length upto 5 whose connected components were chains. We also gave a new insertion encoding and bijection that we used to completely classify shape-Wilf equivalence of sets of short patterns.