Priyavrat Deshpande

activity

20112026

most citedArrangements of Submanifolds and the Tangent Bundle Complement

12 citations · 37 across the 25 of their papers we have counts for

collaborators

Showing math.COShow all

15 papers · 1 filter

math.CO2026

Spectral properties of the resistance Laplacian with applications to data clustering and anomaly detection

Priyavrat Deshpande, Gargi Lather

The resistance Laplacian is a graph matrix associated with the effective resistance metric and provides a global counterpart of the classical graph Laplacian. Although it inherits…

math.CO2026

On a complete characterization of path-free complexes associated with complete multipartite graphs

Priyavrat Deshpande, Shuchita Goyal, Rutuja Sawant

Let $G$ be a graph and let $\PF_t(G)$ denote the simplicial complex whose faces are vertex subsets whose induced subgraphs contain no path on $t$ vertices. These complexes encode a…

math.CO2026

Vertex decomposable complexes of directed forests, conflict graphs and chordality

Priyavrat Deshpande, Rutuja Sawant

Let $D$ be a multidigraph. We study the simplicial complex $Dlf (D)$ , whose vertices are the directed edges of $D$ and whose faces correspond to directed linear forests, th…

math.CO2025

The complex of $r$ -co-connected subgraphs, chordality and Fröberg's theorem

Priyavrat Deshpande, Amit Roy, Rutuja Sawant

We introduce a new family of pure simplicial complexes, called the $r$ -co-connected complex of $G$ with respect to $A$ , $Σ_{r} (A, G)$ , where $r \geq 1$ is a natural number, $G$ is a si…

math.CO2023

Sketches, moves and partitions: counting regions of deformations of reflection arrangements

Priyavrat Deshpande, Krishna Menon

The collection of reflecting hyperplanes of a finite Coxeter group is called a reflection arrangement and it appears in many subareas of combinatorics and representation theory. We…

math.CO2022★ 1 cited

Refinements of the braid arrangement and two parameter Fuss-Catalan numbers

Priyavrat Deshpande, Krishna Menon, Writika Sarkar

A hyperplane arrangement in $R^{n}$ is a finite collection of affine hyperplanes. Counting regions of hyperplane arrangements is an active research direction in enumerative…

math.CO2021★ 2 cited

A branch statistic for trees: Interpreting coefficients of the characteristic polynomial of braid deformations

Priyavrat Deshpande, Krishna Menon

A hyperplane arrangement in $R^{n}$ is a finite collection of affine hyperplanes. The regions are the connected components of the complement of these hyperplanes. By a theor…

math.CO2021

The moment polytope of the abelian polygon space

Navnath Daundkar, Priyavrat Deshpande

The moduli space of $n$ chains in the plane with generic side lengths that terminate on a fixed line is a smooth, closed manifold of dimension $n - 1$ . This manifold is also equipped…

math.CO2021★ 6 cited

Chordal graphs, higher independence and vertex decomposable complexes

Fred M. Abdelmalek, Priyavrat Deshpande, Shuchita Goyal +2

Given a simple undirected graph $G$ there is a simplicial complex $Ind (G)$ , called the independence complex, whose faces correspond to the independent sets of $G$ . This is…

math.CO2021

A combinatorial statistic for labeled threshold graphs

Priyavrat Deshpande, Krishna Menon, Anurag Singh

Consider the collection of hyperplanes in $R^{n}$ whose defining equations are given by ${x_{i} + x_{j} = 0 ∣ 1 \leq i < j \leq n}$ . This arrangement is called the threshold arr…

math.CO2021★ 1 cited

Counting regions of the boxed threshold arrangement

Priyavrat Deshpande, Krishna Menon, Anurag Singh

In this paper we consider the hyperplane arrangement in $R^{n}$ whose hyperplanes are ${x_{i} + x_{j} = 1 ∣ 1 \leq i < j \leq n} \cup {x_{i} = 0, 1 ∣ 1 \leq i \leq n}$ . We call it…

math.CO2020

Distance $r$ -domination number and $r$ -independence complexes of graphs

Priyavrat Deshpande, Samir Shukla, Anurag Singh

For $r \geq 1$ , the $r$ -independence complex of a graph $G$ , denoted Ind $_{r} (G)$ , is a simplicial complex whose faces are subsets $A \subseteq V (G)$ such that each component of the i…

math.CO2014

Face enumeration for line arrangements in a $2$ -torus

Karthik Chandrashekhar, Priyavrat Deshpande

A toric arrangement is a finite collection of codimension- $1$ subtori in a torus. These subtori stratify the ambient torus into faces of various dimensions. Let $f_{i}$ denote the nu…

math.CO2012

On Arrangements of Pseudohyperplanes

Priyavrat Deshpande

To every realizable oriented matroid there corresponds an arrangement of real hyperplanes. The homeomorphism type of the complexified complement of such an arrangement is completel…

math.CO2011★ 6 cited

On a Generalization of Zaslavsky's Theorem for Hyperplane Arrangements

Priyavrat Deshpande

We define arrangements of codimension-1 submanifolds in a smooth manifold which generalize arrangements of hyperplanes. When these submanifolds are removed the manifold breaks up i…

Spectral properties of the resistance Laplacian with applications to data clustering and anomaly detection

On a complete characterization of path-free complexes associated with complete multipartite graphs

Vertex decomposable complexes of directed forests, conflict graphs and chordality

The complex of r-co-connected subgraphs, chordality and Fröberg's theorem

Sketches, moves and partitions: counting regions of deformations of reflection arrangements

Refinements of the braid arrangement and two parameter Fuss-Catalan numbers

A branch statistic for trees: Interpreting coefficients of the characteristic polynomial of braid deformations

The moment polytope of the abelian polygon space

Chordal graphs, higher independence and vertex decomposable complexes

A combinatorial statistic for labeled threshold graphs

Counting regions of the boxed threshold arrangement

Distance r-domination number and r-independence complexes of graphs

Face enumeration for line arrangements in a 2-torus

On Arrangements of Pseudohyperplanes

On a Generalization of Zaslavsky's Theorem for Hyperplane Arrangements

The complex of $r$ -co-connected subgraphs, chordality and Fröberg's theorem

Distance $r$ -domination number and $r$ -independence complexes of graphs

Face enumeration for line arrangements in a $2$ -torus