Hiranya Kishore Dey

activity

20182026

most citedOn Difference of Enhanced Power Graph and Power Graph of a Finite Group

7 citations · 9 across the 25 of their papers we have counts for

collaborators

25 papers

math.CO2026

How to pick your team with no size restriction

Hiranya Kishore Dey

Settling a problem raised by Eccles in 2015, Narayanan in 2026 considers a two-player game in which two captains alternately select players while the opponent decides to which team…

math.GR2026

Group Structure from Subgroup and Cyclic Subgroup Counts

Angsuman Das, Hiranya Kishore Dey, Cesar Galindo +1

For a finite group $G$, let $\sub(G)$ be the number of subgroups of $G$, let $\cyc(G)$ be the number of cyclic subgroups, and let $π(G)$ be the number of distinct prime d…

math.CO2025

$q$ -analogues of Fisher's inequality and oddtown theorem

Hiranya Kishore Dey

A classical result in design theory, known as Fisher's inequality, states that if every pair of clubs in a town shares the same number of members, then the number of clubs cannot e…

math.CO2024

A descent-excedance correspondence in colored permutation groups

Hiranya Kishore Dey, Umesh Shankar, Sivaramakrishnan Sivasubramanian

It is well known that descents and excedances are equidistributed in the symmetric group. We show that the descent and excedance enumerators, summed over permutations with a fixed…

math.CO2024

Sign-balance of excedances over mod-k-alternating permutations and gamma-positivity

Hiranya Kishore Dey, Iswar Mahato

A permutation is called mod-k-alternating if its entries are restricted to having the same remainder as the index, modulo some integer $k \geq 1.$ In this paper, we find the sign-b…

math.RT2024

How large is the character degree sum compared to the character table sum for a finite group?

Arvind Ayyer, Hiranya Kishore Dey, Digjoy Paul

In 1961, Solomon gave upper and lower bounds for the sum of all the entries in the character table of a finite group in terms of elementary properties of the group. In a different…

math.CO2024

An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups

Sudip Bera, Hiranya Kishore Dey

The enhanced power graph of a group $G$ is a graph with vertex set $G,$ where two distinct vertices $x$ and $y$ are adjacent if and only if there exists an element $w$ in $G$ such…

math.GR2023★ 1 cited

On the order sequence of a group

Peter J. Cameron, Hiranya Kishore Dey

This paper provides a bridge between two active areas of research, the spectrum (set of element orders) and the power graph of a finite group. The order sequence of a finite group…

math.CO2023

Sharp lower bound on the "number of nodal decomposition" of graphs

Hiranya Kishore Dey, Soumyajit Saha

Urschel introduced a notion of nodal partitioning to prove an upper bound on the number of nodal decomposition of discrete Laplacian eigenvectors. The result is an analogue to the…

math.CO2023★ 1 cited

Distance matrix of enhanced power graphs of finite groups

Anita Arora, Hiranya Kishore Dey, Shivani Goel

The enhanced power graph of a group $G$ is the graph $G_{E} (G)$ with vertex set $G$ and edge set $ \{(u,v): u, v \in \langle w \rangle,~\mbox{for some}~ w \in G\}$. In this…

math.GR2022

The solvability of a finite group by the sum of powers of element orders

Hiranya Kishore Dey

We prove a new criterion for the solvability of the finite groups, depending on the function $ψ_{k} (G)$ which is defined as the sum of $k$ -th powers of the element orders of $G$ . We…

math.CO2022

$q$ -enumeration of type B and D Eulerian polynomials based on parity of descents

Hiranya Kishore Dey, Umesh Shankar, Sivaramakrishnan Sivasubramanian

Carlitz and Scoville in 1973 considered a four variable polynomial that enumerates permutations in $S_{n}$ with respect to the parity of its descents and ascents. In recen…

math.GR2022

An exact upper bound for the sum of powers of element orders in non-cyclic finite groups

Hiranya Kishore Dey, Archita Mondal

For a finite group $G$ , let $ψ (G)$ denote the sum of element orders of $G$ . This function was introduced by Amiri, Amiri, and Isaacs in 2009 and they proved that for any finite gro…

math.CO2022★ 7 cited

On Difference of Enhanced Power Graph and Power Graph of a Finite Group

Sucharita Biswas, Peter J. Cameron, Angsuman Das +1

The difference graph $D (G)$ of a finite group $G$ is the difference of enhanced power graph of $G$ and power graph of $G$ , with all isolated vertices are removed. In this paper we…

math.CO2021

The Young matroid: A multiset extension of the Catalan matroid to arbitrary Young diagrams

Hiranya Kishore Dey, Brahadeesh Sankarnarayanan, S. Venkitesh

Introduced by Ardila (J. Combin. Theory Ser. A, 2003), the Catalan matroid is obtained by defining the bases of the matroid using Dyck paths from $(0, 0)$ to $(n, n)$ . Further resear…

math.CO2021

On connectivity, domination number and spectral radius of the proper enhanced power graphs of finite nilpotent groups

Sudip Bera, Hiranya Kishore Dey

For a group $G,$ the enhanced power graph of $G$ is a graph with vertex set $G$ in which two distinct elements $x, y$ are adjacent if and only if there exists an element $w$ in $G$ …

math.CO2020

Combinatorial proof of the log-convexity for the derangements in the Coxeter groups

Hiranya Kishore Dey, Subhajit Ghosh

We provide the combinatorial proofs of the log-convexity for the derangement numbers in the symmetric group $S_{n}$ , hyperoctahedral group $B_{n}$ , and the demihy…

math.CO2020

Log-concavity of the Excedance Enumerators in positive elements of Type A and Type B Coxeter Groups

Hiranya Kishore Dey

The classical Eulerian Numbers $A_{n, k}$ are known to be log-concave. Let $P_{n, k}$ and $Q_{n, k}$ be the number of even and odd permutations with $k$ excedances. In this paper, we…

math.CO2020

Signed Alternating-runs enumeration in Classical Weyl Groups

Hiranya Kishore Dey, Sivaramakrishnan Sivasubramanian

The alternating-runs polynomial enumerates alternating runs in the symmetric group. There are three formulae for the number of permutations, $R_{n, k}$ in $S_{n}$ with $k$ …

math.CO2020

Determining Number of Kneser Graphs: Exact Values and Improved Bounds

Angsuman Das, Hiranya Kishore Dey

The determining number of a graph $G = (V, E)$ is the minimum cardinality of a set $S \subseteq V$ such that pointwise stabilizer of $S$ under the action of $A u t (G)$ is trivial. In t…

math.CO2020

On the Alternating runs polynomial in type B and D Coxeter Groups

Hiranya Kishore Dey, Sivaramakrishnan Sivasubramanian

Wilf showed that the the alternating runs polynomial $R_{n} (t)$ counting the number of permutations in the Symmetric group is divisible by $(1 + t)^{m}$ where $m = \lfloor (n-2)/2 \rfloo…

math.CO2020

On the connectivity of enhanced power graph of finite group

Sudip Bera, Hiranya Kishore Dey, Sajal Kumar Mukherjee

This paper deals with the vertex connectivity of enhanced power graph of finite group. We classify all abelian groups G such that vertex connectivity of enhanced power graph of G i…

math.CO2020

Eulerian Central Limit Theorems and Carlitz identities in positive elements of Classical Weyl Groups

Hiranya Kishore Dey, Sivaramakrishnan Sivasubramanian

Central Limit Theorems are known for the Eulerian statistic "descent" (or "excedance") in the symmetric group $\SSS_n$. Recently, Fulman, Kim, Lee and Petersen gave a Central Limit…

math.CO2018

Gamma positivity of the Excedance based Eulerian polynomial in positive elements of Classical Weyl Groups

Hiranya Kishore Dey, Sivaramakrishnan Sivasubramanian

The classical Eulerian polynomials $A_{n} (t)$ are known to be gamma positive. Define the positive Eulerian polynomial $AEx c^{+}_{n} (t)$ as the polynomial obtained when we sum…

How to pick your team with no size restriction

Group Structure from Subgroup and Cyclic Subgroup Counts

q-analogues of Fisher's inequality and oddtown theorem

A descent-excedance correspondence in colored permutation groups

Sign-balance of excedances over mod-k-alternating permutations and gamma-positivity

How large is the character degree sum compared to the character table sum for a finite group?

An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups

On the order sequence of a group

Sharp lower bound on the "number of nodal decomposition" of graphs

Distance matrix of enhanced power graphs of finite groups

The solvability of a finite group by the sum of powers of element orders

q-enumeration of type B and D Eulerian polynomials based on parity of descents

An exact upper bound for the sum of powers of element orders in non-cyclic finite groups

On Difference of Enhanced Power Graph and Power Graph of a Finite Group

The Young matroid: A multiset extension of the Catalan matroid to arbitrary Young diagrams

On connectivity, domination number and spectral radius of the proper enhanced power graphs of finite nilpotent groups

Combinatorial proof of the log-convexity for the derangements in the Coxeter groups

Log-concavity of the Excedance Enumerators in positive elements of Type A and Type B Coxeter Groups

Signed Alternating-runs enumeration in Classical Weyl Groups

Determining Number of Kneser Graphs: Exact Values and Improved Bounds

On the Alternating runs polynomial in type B and D Coxeter Groups

On the connectivity of enhanced power graph of finite group

Eulerian Central Limit Theorems and Carlitz identities in positive elements of Classical Weyl Groups

Gamma positivity of the Excedance based Eulerian polynomial in positive elements of Classical Weyl Groups

$q$ -analogues of Fisher's inequality and oddtown theorem

$q$ -enumeration of type B and D Eulerian polynomials based on parity of descents