Mudit Aggarwal

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20222026

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math.CO2026

On groups with D-finite cogrowth series

Mudit Aggarwal, Murray Elder, Andrew Rechnitzer

The cogrowth series of a group with respect to a finite generating set is an important combinatorial quantity that seems very difficult to compute exactly, as evidenced by the scar…

math.CO2026

Straight polyomino tilings of rectangles and special rim-hook tableaux

Mudit Aggarwal, Hrishik Koley, Samrith Ram

We derive explicit rational generating functions for weighted tilings of $2 k \times n$ rectangles by straight $k \times 1$ tiles. Our approach combines a decomposition by fault lines…

math.CO2022

Generating functions for straight polyomino tilings of narrow rectangles

Mudit Aggarwal, Samrith Ram

Let $m, k$ be fixed positive integers. Determining the generating function for the number of tilings of an $m \times n$ rectangle by $k \times 1$ rectangles is a long-standing open pr…