Shahriar Shahriari
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Shahriar Shahriari has a total of 41 co-authors. Here are the top co-authors by number of shared publications:
- Ghassan Sarkis
Department of Mathematics Pomona College 91711 Claremont CA USA
3 shared publications - Ameera Chowdhury
Department of Mathematical Sciences Carnegie Mellon University 15213 Pittsburgh PA USA
2 shared publications - Andreea Cristina Nicolae
ZAS Berlin
2 shared publications - Dan Kalman
American University Washington, D.C. 20016
2 shared publications - Elinor Gardner Escamilla
Pomona College
2 shared publications - Gabriel Currier
University of British Columbia
2 shared publications
Latest Publications
- Open Access
- 11 April 2025
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 32 (2) , P2.31
3-Cluster-Free Families of Subspaces
Three $k$-dimensional subspaces $A$, $B$, and $C$ of an $n$-dimensional vector space $V$ over a finite field are called a $3$-cluster if $A \cap B \cap C = \{\mathbf{0}_V\}$ and yet $\dim(A+B+C) \leq 2k$. A special kind of $3$-cluster, which we call a covering triple, consists of subspaces $A,B,C$ such that $A = (A \cap B )\oplus (A \cap C)$. We prove that, for $2 \leq k \le n/2$, the largest size of a covering triple-free family of $k$-dimensional subspaces is the same as the size of the largest such star (a family of subspaces all containing a designated non-zero vector). Moreover, we show that if $k < n/2$, then stars are the only families achieving this largest size. This in turn implies the same result for $3$-clusters, which gives the vector space-analogue of a theorem of Mubayi for set systems.- 11 April 2025
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 32 (2) , P2.31
Open Access3-Cluster-Free Families of Subspaces
Three $k$-dimensional subspaces $A$, $B$, and $C$ of an $n$-dimensional vector space $V$ over a finite field are called a $3$-cluster if $A \cap B \cap C = \{\mathbf{0}_V\}$ and yet $\dim(A+B+C) \leq 2k$. A special kind of $3$-cluster, which we call a covering triple, consists of subspaces $A,B,C$ such that $A = (A \cap B )\oplus (A \cap C)$. We prove that, for $2 \leq k \le n/2$, the largest size of a covering triple-free family of $k$-dimensional subspaces is the same as the size of the largest such star (a family of subspaces all containing a designated non-zero vector). Moreover, we show that if $k < n/2$, then stars are the only families achieving this largest size. This in turn implies the same result for $3$-clusters, which gives the vector space-analogue of a theorem of Mubayi for set systems. - Open Access
$3$-cluster-free families of subspaces
Three $k$-dimensional subspaces $A$, $B$, and $C$ of an $n$-dimensional vector space $V$ over a finite field are called a $3$-cluster if $A \cap B \cap C = \{\mathbf{0}_V\}$ and yet $\dim(A+B+C) \leq 2k$. A special kind of $3$-cluster, which we call a covering triple, consists of subspaces $A,B,C$ such that $A = (A \cap B )\oplus (A \cap C)$. We prove that, for $2 \leq k \le n/2$, the largest size of a covering triple-free family of $k$-dimensional subspaces is the same as the size of the largest such star (a family of subspaces all containing a designated non-zero vector). Moreover, we show that if $k < n/2$, then stars are the only families achieving this largest size. This in turn implies the same result for $3$-clusters, which gives the vector space-analogue of a theorem of Mubayi for set systems.Open Access$3$-cluster-free families of subspaces
Three $k$-dimensional subspaces $A$, $B$, and $C$ of an $n$-dimensional vector space $V$ over a finite field are called a $3$-cluster if $A \cap B \cap C = \{\mathbf{0}_V\}$ and yet $\dim(A+B+C) \leq 2k$. A special kind of $3$-cluster, which we call a covering triple, consists of subspaces $A,B,C$ such that $A = (A \cap B )\oplus (A \cap C)$. We prove that, for $2 \leq k \le n/2$, the largest size of a covering triple-free family of $k$-dimensional subspaces is the same as the size of the largest such star (a family of subspaces all containing a designated non-zero vector). Moreover, we show that if $k < n/2$, then stars are the only families achieving this largest size. This in turn implies the same result for $3$-clusters, which gives the vector space-analogue of a theorem of Mubayi for set systems. - 26 July 2022
- Published by Elsevier in Journal of Algebra
- Vol. 610, 199-222
On torsion elements and their annihilators
- 26 July 2022
- Published by Elsevier in Journal of Algebra
- Vol. 610, 199-222
On torsion elements and their annihilators
- 29 June 2022
- Published by Taylor & Francis in PRIMUS
- Vol. 33 (5) , 445-462
Community, Collaboration, and Climate
The Department of Mathematics & Statistics at Pomona College has long worked to create an inclusive and welcoming space for all individuals to study mathematics. Many years ago, our approach to the lack of diversity we saw in our majors was remediation through programming which sought to ameliorate student deficits. More recently, however, we have taken an anti-deficit approach with focus on changes to the department itself. The programs we have implemented are described below as enhancing community, collaboration, and climate within our department.
- 29 June 2022
- Published by Taylor & Francis in PRIMUS
- Vol. 33 (5) , 445-462
Community, Collaboration, and Climate
The Department of Mathematics & Statistics at Pomona College has long worked to create an inclusive and welcoming space for all individuals to study mathematics. Many years ago, our approach to the lack of diversity we saw in our majors was remediation through programming which sought to ameliorate student deficits. More recently, however, we have taken an anti-deficit approach with focus on changes to the department itself. The programs we have implemented are described below as enhancing community, collaboration, and climate within our department.
- 24 July 2019
- Published by Springer Nature in Order
- Vol. 37 (2) , 223-242
Avoiding Brooms, Forks, and Butterflies in the Linear Lattices
- 24 July 2019
- Published by Springer Nature in Order
- Vol. 37 (2) , 223-242
Avoiding Brooms, Forks, and Butterflies in the Linear Lattices
- 4 December 2018
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 68 (8) , 1642-1654
Nowhere–zero bases for the nullspace of the incidence matrices of graphs
A nowhere-zero k-flow for a directed or undirected graph is a vector in the nullspace of the incidence matrix of the graph such that all the entries of the vector are from the set . We consider the problem of finding a basis consisting of nowhere-zero k-flows for the nullspace of the incidence matrix. For a variety of graphs—including the complete graphs—we find such bases with k=2 or k=3. We prove that all directed graphs with no cut-edge have such a basis with k=12, and conjecture that 12 can be replaced with 5. If true, this would strengthen Tutte's celebrated conjecture on nowhere-zero 5-flows. For undirected graphs that have some nowhere-zero k-flow, we prove the existence of a basis of nowhere-zero 36-flows and conjecture that 36 can be replaced with 6.
- 4 December 2018
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 68 (8) , 1642-1654
Nowhere–zero bases for the nullspace of the incidence matrices of graphs
A nowhere-zero k-flow for a directed or undirected graph is a vector in the nullspace of the incidence matrix of the graph such that all the entries of the vector are from the set . We consider the problem of finding a basis consisting of nowhere-zero k-flows for the nullspace of the incidence matrix. For a variety of graphs—including the complete graphs—we find such bases with k=2 or k=3. We prove that all directed graphs with no cut-edge have such a basis with k=12, and conjecture that 12 can be replaced with 5. If true, this would strengthen Tutte's celebrated conjecture on nowhere-zero 5-flows. For undirected graphs that have some nowhere-zero k-flow, we prove the existence of a basis of nowhere-zero 36-flows and conjecture that 36 can be replaced with 6.
- 1 January 2015
- Published by Elsevier in Finite Fields and Their Applications
- Vol. 31, 108-120
Zero-sum flows of the linear lattice
- 1 January 2015
- Published by Elsevier in Finite Fields and Their Applications
- Vol. 31, 108-120
Zero-sum flows of the linear lattice
- 1 November 2014
- Published by Elsevier in Journal of Combinatorial Theory, Series A
- Vol. 128, 84-103
The Manickam–Miklós–Singhi conjectures for sets and vector spaces
- 1 November 2014
- Published by Elsevier in Journal of Combinatorial Theory, Series A
- Vol. 128, 84-103
The Manickam–Miklós–Singhi conjectures for sets and vector spaces
- Open Access
A New Quadratic Bound for the Manickam-Miklós-Singhi Conjecture
More than twenty-five years ago, Manickam, Miklos, and Singhi conjectured that for positive integers $n,k$ with $n \geq 4k$, every set of $n$ real numbers with nonnegative sum has at least $\binom{n-1}{k-1}$ $k$-element subsets whose sum is also nonnegative. We verify this conjecture when $n \geq 8k^2$, which simultaneously improves and simplifies a bound of Alon, Huang, and Sudakov and also a bound of Pokrovskiy when $k < 10^{45}$.Open AccessA New Quadratic Bound for the Manickam-Miklós-Singhi Conjecture
More than twenty-five years ago, Manickam, Miklos, and Singhi conjectured that for positive integers $n,k$ with $n \geq 4k$, every set of $n$ real numbers with nonnegative sum has at least $\binom{n-1}{k-1}$ $k$-element subsets whose sum is also nonnegative. We verify this conjecture when $n \geq 8k^2$, which simultaneously improves and simplifies a bound of Alon, Huang, and Sudakov and also a bound of Pokrovskiy when $k < 10^{45}$. - Open Access
The Manickam-Miklós-Singhi Conjectures for Sets and Vector Spaces
More than twenty-five years ago, Manickam, Mikl\'{o}s, and Singhi conjectured that for positive integers $n,k$ with $n \geq 4k$, every set of $n$ real numbers with nonnegative sum has at least $\binom{n-1}{k-1}$ $k$-element subsets whose sum is also nonnegative. We verify this conjecture when $n \geq 8k^{2}$, which simultaneously improves and simplifies a bound of Alon, Huang, and Sudakov and also a bound of Pokrovskiy when $k < 10^{45}$. Moreover, our arguments resolve the vector space analogue of this conjecture. Let $V$ be an $n$-dimensional vector space over a finite field. Assign a real-valued weight to each $1$-dimensional subspace in $V$ so that the sum of all weights is zero. Define the weight of a subspace $S \subset V$ to be the sum of the weights of all the $1$-dimensional subspaces it contains. We prove that if $n \geq 3k$, then the number of $k$-dimensional subspaces in $V$ with nonnegative weight is at least the number of $k$-dimensional subspaces in $V$ that contain a fixed $1$-dimensional subspace. This result verifies a conjecture of Manickam and Singhi from 1988.Open AccessThe Manickam-Miklós-Singhi Conjectures for Sets and Vector Spaces
More than twenty-five years ago, Manickam, Mikl\'{o}s, and Singhi conjectured that for positive integers $n,k$ with $n \geq 4k$, every set of $n$ real numbers with nonnegative sum has at least $\binom{n-1}{k-1}$ $k$-element subsets whose sum is also nonnegative. We verify this conjecture when $n \geq 8k^{2}$, which simultaneously improves and simplifies a bound of Alon, Huang, and Sudakov and also a bound of Pokrovskiy when $k < 10^{45}$. Moreover, our arguments resolve the vector space analogue of this conjecture. Let $V$ be an $n$-dimensional vector space over a finite field. Assign a real-valued weight to each $1$-dimensional subspace in $V$ so that the sum of all weights is zero. Define the weight of a subspace $S \subset V$ to be the sum of the weights of all the $1$-dimensional subspaces it contains. We prove that if $n \geq 3k$, then the number of $k$-dimensional subspaces in $V$ with nonnegative weight is at least the number of $k$-dimensional subspaces in $V$ that contain a fixed $1$-dimensional subspace. This result verifies a conjecture of Manickam and Singhi from 1988.