Dinesh Kumar

collaborators

9 papers

math.CO2026

Structural Classification of a Graph with Independence Number Five

Manisha Kumari, Dinesh Kumar

The independence polynomial of a simple graph $G$ is given by $ I_G(z) = i_0 + i_1 z + i_2 z^2 + \cdots + i_αz^α$, where $ i_α$ denotes the size of a maximum independent set, a…

math.DS2026

A survey on permutable transcendental entire functions and their dynamics

Dinesh Kumar

In this paper, we survey important results on the dynamics of permutable transcendental entire functions from 1958 to 2025. We have discussed the forms of transcendental entire fun…

math.DS2026

Results on the postsingular set of compositions of transcendental entire functions

Manisha Kumari, Dinesh Kumar

In this paper, we study the dynamics of commuting transcendental entire functions $f$ and $g$ , where $g = a f^{p} + b$ with $a, b \in C$ , $p \in N$ , and $a \neq = 0, 1$ . We exami…

math.DS2026

Equality of the dynamical sets of two commuting transcendental entire functions

Manisha Kumari, Dinesh Kumar

In this paper, we study the dynamics of commuting transcendental entire functions $f$ and $g$ , where $g$ is of the form $a f^{p} + b$ with $a,b \in \C$, $p \in N$ , and $a \neq = 0, 1$ .…

cs.LG2026

Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics

Bhaskar Ranjan Karn, Dinesh Kumar

Complex dynamical systems governed by holomorphic maps such as $z^{2} + c$ exhibit fractal boundaries with extreme sensitivity to initial conditions. Accurately modelling these struc…

math.NT2026

Inverses of six classes of permutation polynomials of the form $x + I^^{3} Tr_{q}^{q^{2}} (h (x))$ over finite fields of even characteristic

Rajesh P. Singh, Dinesh Kumar, Jitendra Prakash

Recently, Jiang et al. \cite{JIANG2025102522} obtained several classes of Permutation Polynomial of the form $x + I^^{3} Tr_{q}^{q^{2}} (h (x))$ over finite fields $\mathbb{F}_{q…

Structural Classification of a Graph with Independence Number Five

A survey on permutable transcendental entire functions and their dynamics

Results on the postsingular set of compositions of transcendental entire functions

Equality of the dynamical sets of two commuting transcendental entire functions

Holomorphic Neural ODEs with Kolmogorov-Arnold Networks for Interpretable Discovery of Complex Dynamics

Inverses of six classes of permutation polynomials of the form x+I^3Trqq2​(h(x)) over finite fields of even characteristic

Inverses of six classes of permutation polynomials of the form $x + I^^{3} Tr_{q}^{q^{2}} (h (x))$ over finite fields of even characteristic