Divya Aggarwal

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math.CO2023

Enumeration of splitting subsets of endofunctions on finite sets

Divya Aggarwal

Let $d$ and $n$ be positive integers such that $d ∣ n$ . Let $[n] = {1, 2, \dots, n}$ and $T$ be an endofunction on $[n]$ . A subset $W$ of $[n]$ of cardinality $n / d$ is said to be $d$ -s…

math.CO2021

Polynomial Matrices, Splitting Subspaces and Krylov Subspaces over Finite Fields

Divya Aggarwal, Samrith Ram

Let $T$ be a linear operator on an $F_{q}$ -vector space $V$ of dimension $n$ . For any divisor $m$ of $n$ , an $m$ -dimensional subspace $W$ of $V$ is $T$ -splitting if $$ V =W\…

math.CO2021

Splitting Subspaces of Linear Operators over Finite Fields

Divya Aggarwal, Samrith Ram

Let $V$ be a vector space of dimension $N$ over the finite field $F_{q}$ and $T$ be a linear operator on $V$ . Given an integer $m$ that divides $N$ , an $m$ -dimensional subsp…