arXiv subjects

Pragya Verma

Publications and source records attributed to Pragya Verma.

5 recordsLinked to original sources

arXiv2026

Linear Tur\'an Numbers of Uniform Hypertrees

A hypergraph is \emph{linear} if every pair of vertices is contained in at most one hyperedge. For a family $\mathcal{F}$ of $r$-uniform hypergraphs, let $\operatorname{ex}^{\mathrm{lin}}_r(n,\mathcal{F})$ denote the maximum number of hyperedges in an $n$-vertex $\mathcal{F}$-free linear $r$-uniform hypergraph. Extending earlier work on acyclic triple systems, we study linear Tur\'an numbers of uniform hypertrees in higher uniformity. For the linear star $S_k^r$, we prove \[ \operatorname{ex}^{\mathrm{lin}}_r(n,S_k^r)\leq \frac{n(k-1)}{r}, \] with equality precisely for $(k-1)$-regular linear $r$-uniform hypergraphs, whenever such hypergraphs exist. Under suitable divisibility and design-existence assumptions, we also construct $T_k^r$-free hypergraphs with $n(k-1)/r$ edges for every linear $r$-uniform hypertree $T_k^r$ with $k$ hyperedges. For the four-edge broom $B_4^r$, we prove \[ \operatorname{ex}^{\mathrm{lin}}_r(n,B_4^r)\leq \frac{(r+1)n}{r}, \] with equality exactly for disjoint unions of Steiner systems $S(2,r,r^2)$, whenever such systems exist. For the crown $E_4^r$, we establish a degree-sensitive upper bound implying \[ \operatorname{ex}^{\mathrm{lin}}_r(n,E_4^r)\leq \frac{(2r-1)n}{r}, \] and give a lower-bound construction leaving a constant-factor gap. Finally, we settle the linear Tur\'an problem for the four-edge path $P_4^r$ in every uniformity: \[ \operatorname{ex}^{\mathrm{lin}}_r(n,P_4^r)\leq \frac{(r+1)n}{r}. \] Equality holds precisely for disjoint unions of Steiner systems $S(2,r,r^2)$. We also give counterexamples to a key structural claim used in a previously proposed proof of the $4$-uniform case.

math.CO↗

arXiv2026

Bounds on Linear Tur\'{a}n Number for Trees

A hypergraph $H$ is said to be \emph{linear} if every pair of vertices lies in at most one hyperedge. Given a family $\mathcal{F}$ of $r$-uniform hypergraphs, an $r$-uniform hypergraph $H$ is said to be \emph{$\mathcal{F}$-free} if it contains no member of $\mathcal{F}$ as a subhypergraph. The \emph{linear Tur\'{a}n number} $ex_r^{\mathrm{lin}}(n,\mathcal{F})$ denotes the maximum number of hyperedges in an $\mathcal{F}$-free linear $r$-uniform hypergraph on $n$ vertices. Gy\'arf\'as, Ruszink\'o, and S\'ark\"ozy~[\emph{Linear Tur\'an numbers of acyclic triple systems}, European J.\ Combin.\ (2022)] initiated the study of bounds on the linear Tur\'an number for acyclic $3$-uniform linear hypergraphs. In this paper, we extend the study of linear Tur\'{a}n numbers for acyclic systems to higher uniformity. We first give a construction for linear $r$-uniform trees with $k$ edges that yields the lower bound $ ex_r^{\mathrm{lin}}(n,T_k^r)\ge {n(k-1)}/{r}, $ under mild divisibility and existence assumptions. Next, we study hypertrees with four edges. We prove the exact bound $ ex_r^{\mathrm{lin}}(n,B_4^r)\le {(r+1)n}/{r} $ and characterize the extremal hypergraph class, where $B_4^r$ is formed from $S_3^r$ by appending a hyperedge incident to a degree-one vertex. We also prove the bound $ ex_r^{\mathrm{lin}}(n,E_4^r)\le {(2r-1)n}/{r} $ for the crown $E_4^r$. Finally, we give a construction showing $ ex_r^{\mathrm{lin}}(n,P_4^r)\ge {(r+1)n}/{r} $ under suitable assumptions and conclude with a conjecture on sharp upper bound for $P_4^r$.

math.CO↗

arXiv2025

An Empirical Investigation of the Experiences of Dyslexic Software Engineers

Dyslexia is a common learning disorder that primarily impairs an individual's reading and writing abilities. In adults, dyslexia can affect both professional and personal lives, often leading to mental challenges and difficulties acquiring and keeping work. In Software Engineering (SE), reading and writing difficulties appear to pose substantial challenges for core tasks such as programming. However, initial studies indicate that these challenges may not significantly affect their performance compared to non-dyslexic colleagues. Conversely, strengths associated with dyslexia could be particularly valuable in areas like programming and design. However, there is currently no work that explores the experiences of dyslexic software engineers, and puts their strengths into relation with their difficulties. To address this, we present a qualitative study of the experiences of dyslexic individuals in SE. We followed the basic stage of the Socio-Technical Grounded Theory method and base our findings on data collected through 10 interviews with dyslexic software engineers, 3 blog posts and 153 posts on the social media platform Reddit. We find that dyslexic software engineers especially struggle at the programming learning stage, but can succeed and indeed excel at many SE tasks once they master this step. Common SE-specific support tools, such as code completion and linters are especially useful to these individuals and mitigate many of the experienced difficulties. Finally, dyslexic software engineers exhibit strengths in areas such as visual thinking and creativity. Our findings have implications to SE practice and motivate several areas of future research in SE, such as investigating what makes code less/more understandable to dyslexic individuals.

cs.SE↗

arXiv2025

Differences between Neurodivergent and Neurotypical Software Engineers: Analyzing the 2022 Stack Overflow Survey

Neurodiversity describes variation in brain function among people, including common conditions such as Autism spectrum disorder (ASD), Attention deficit hyperactivity disorder (ADHD), and dyslexia. While Software Engineering (SE) literature has started to explore the experiences of neurodivergent software engineers, there is a lack of research that compares their challenges to those of neurotypical software engineers. To address this gap, we analyze existing data from the 2022 Stack Overflow Developer survey that collected data on neurodiversity. We quantitatively compare the answers of professional engineers with ASD (n=374), ADHD (n=1305), and dyslexia (n=363) with neurotypical engineers. Our findings indicate that neurodivergent engineers face more difficulties than neurotypical engineers. Specifically, engineers with ADHD report that they face more interruptions caused by waiting for answers, and that they less frequently interact with individuals outside their team. This study provides a baseline for future research comparing neurodivergent engineers with neurotypical ones. Several factors in the Stack Overflow survey and in our analysis are likely to lead to conservative estimates of the actual effects between neurodivergent and neurotypical engineers, e.g., the effects of the COVID-19 pandemic and our focus on employed professionals.

cs.SE↗

arXiv2025

CoVoL: A Cooperative Vocabulary Learning Game for Children with Autism

Children with Autism commonly face difficulties in vocabulary acquisition, which can have an impact on their social communication. Using digital tools for vocabulary learning can prove beneficial for these children, as they can provide a predictable environment and effective individualized feedback. While existing work has explored the use of technology-assisted vocabulary learning for children with Autism, no study has incorporated turn-taking to facilitate learning and use of vocabulary similar to that used in real-world social contexts. To address this gap, we propose the design of a cooperative two-player vocabulary learning game, CoVoL. CoVoL allows children to engage in game-based vocabulary learning useful for real-world social communication scenarios. We discuss our first prototype and its evaluation. Additionally, we present planned features which are based on feedback obtained through ten interviews with researchers and therapists, as well as an evaluation plan for the final release of CoVoL.

cs.SE↗