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

28 papers

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.NT2025

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning

Priyavrat Deshpande, Aditya Karnataki, Pratiksha Shingavekar

This article presents a comprehensive data-scientific investigation into the arithmetic statistics of congruent number elliptic curves, leveraging a dataset of square-free integers…

math.AC2023

Fröberg's Theorem, vertex splittability and higher independence complexes

Priyavrat Deshpande, Amit Roy, Anurag Singh +1

A celebrated theorem of Fröberg gives a complete combinatorial classification of quadratic square-free monomial ideals with a linear resolution. A generalization of this theorem to…

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.GR2022

On the structure of finitely presented Bestvina-Brady groups

Priyavrat Deshpande, Mallika Roy

Right-angled Artin groups and their subgroups are of great interest because of their geometric, combinatorial and algorithmic properties. It is convenient to define these groups us…

math.AT2022

Building planar polygon spaces from the projective braid arrangement

Navnath Daundkar, Priyavrat Deshpande

The moduli space of planar polygons with generic side lengths is a smooth, closed manifold. It is known that these manifolds contain the real points of the moduli space of distinct…

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.AT2022

Real Bott manifold structure of $n$ -dimensional Klein bottle and its rational Betti numbers

Navnath Daundkar, Priyavrat Deshpande

Donald Davis initiated the study of an $n$ -dimensional analogue of the Klein bottle. This generalized Klein bottle occurs as a moduli space of planar polygons for a certain choice…

math.AT2021

The Borsuk-Ulam theorem for planar polygon spaces

Navnath Daundkar, Priyavrat Deshpande, Shuchita Goyal +1

The moduli space of planar polygons with generic side lengths is a closed, smooth manifold. Mapping a polygon to its reflected image across the $X$ -axis defines a fixed-point-free…

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.AT2020★ 5 cited

Higher Independence Complexes of graphs and their homotopy types

Priyavrat Deshpande, Anurag Singh

For $r \geq 1$ , the $r$ -independence complex of a graph $G$ is a simplicial complex whose faces are subset $I \subseteq V (G)$ such that each component of the induced subgraph $G [I]$ …

math.AT2019

On the topology of bi-cyclopermutohedra

Priyavrat Deshpande, Naageswaran Manikandan, Anurag Singh

Motivated by the work of Panina and her coauthors on cyclopermutohedron we study a poset whose elements correspond to equivalence classes of partitions of the set $\{1,\cdots, n+1\…

math.AT2018★ 2 cited

The Goresky-MacPherson formula for toric arrangements

Priyavrat Deshpande

A subspace arrangement is a finite collection of affine subspaces in $R^{n}$ . One of the main problems associated to arrangements asks up to what extent the topological inva…

math.AT2014★ 1 cited

Coxeter transformation groups and reflection arrangements in smooth manifolds

Ronno Das, Priyavrat Deshpande

Artin groups are a natural generalization of braid groups and are well-understood in certain cases. Artin groups are closely related to Coxeter groups. There is a faithful represen…

math.AT2014★ 1 cited

Deletion-restriction in toric arrangements

Priyavrat Deshpande, Kavita Sutar

Deletion-restriction is a fundamental tool in the theory of hyperplane arrangements. Various important results in this field have been proved using deletion-restriction. In this pa…

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…

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

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning

Fröberg's Theorem, vertex splittability and higher independence complexes

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

On the structure of finitely presented Bestvina-Brady groups

Building planar polygon spaces from the projective braid arrangement

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

Real Bott manifold structure of n-dimensional Klein bottle and its rational Betti numbers

The Borsuk-Ulam theorem for planar polygon spaces

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

Higher Independence Complexes of graphs and their homotopy types

On the topology of bi-cyclopermutohedra

The Goresky-MacPherson formula for toric arrangements

Coxeter transformation groups and reflection arrangements in smooth manifolds

Deletion-restriction in toric arrangements

Face enumeration for line arrangements in a 2-torus

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

Real Bott manifold structure of $n$ -dimensional Klein bottle and its rational Betti numbers

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

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