Related papers: Data Analysis of the Responses to Professor Abigai…
A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations. Let $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ be the set of permutations in the symmetric group $S_n$ which avoids…
It is believed that consistent notation helps the research community in many ways. First and foremost, it provides a consistent interface of communication. Subjective experiments described according to uniform rules are easier to understand…
This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.…
We provide an example of the application of quantitative techniques, tools, and topics from mathematics and data science to analyze the mathematics community itself in order to quantify and document inequity in our discipline. This work is…
We find evidence for the universality of two relative bibliometric indicators of the quality of individual scientific publications taken from different data sets. One of these is a new index that considers both citation and reference…
Name-based gender classification has enabled hundreds of otherwise infeasible scientific studies of gender. Yet, the lack of standardization, proliferation of ad hoc methods, reliance on paid services, understudied limitations, and…
Let G be a finite group. Let pi be a permutation from S{n}. We study the distribution of probabilities of equality a{1} a{2} ...a{n-1}a{n}=a{pi{1}}^{epsilon{1}} a{pi_{2}}^{epsilon{2}}...a{pi{n-1}}^{epsilon_{n-1}} a_{pi_{n}}^{epsilon{n}},…
Mounting evidence suggests that publications and citations of scholars in the STEM fields (Science, Technology, Engineering and Mathematics) suffer from gender biases. In this paper, we study the physics community, a core STEM field in…
This paper explores the paradigm of the differential signature introduced in 1996 by Calabi et al. This methodology has vast implications in fields such as computer vision, where these techniques can potentially be used to verify a person's…
The distribution of the number of academic publications as a function of citation count for a given year is remarkably similar from year to year. We measure this similarity as a width of the distribution and find it to be approximately…
Bibliometric indicators can be determined by comparing specific citation records with the percentiles of a reference set. However, there exists an ambiguity in the computation of percentiles because usually a significant number of papers…
Two alternative accounts can be given of the information contained in the acknowledgments of academic publications. According to the mainstream normative account, the acknowledgments serve to repay debts towards formal or informal…
Beginning with work of Zeilberger on classical pattern counts, there are a variety of structural results for moments of permutation statistics applied to random permutations. Using tools from representation theory, Gaetz and Ryba…
The diversity across outputs generated by LLMs shapes perception of their quality and utility. High lexical diversity is often desirable, but there is no standard method to measure this property. Templated answer structures and ``canned''…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
Efforts to combat continuing gender inequalities in academia need to be informed by evidence about where differences occur. Citations are relevant as potential evidence in appointment and promotion decisions, but it is unclear whether there…
Group-based Trajectory Modeling (GBTM) is applied to the citation curves of articles in six journals and to all citable items in a single field of science (Virology, 24 journals), in order to distinguish among the developmental trajectories…
Google Scholar has been well received by the research community. Its promises of free, universal and easy access to scientific literature as well as the perception that it covers better than other traditional multidisciplinary databases the…
Over 1100 students over four semesters were given the option of taking an introductory undergraduate statistics class either by in-person attendance in lectures or by taking exactly the same class (same instructor, recorded lectures,…
In proof theory the notion of canonical proof is rather basic, and it is usually taken for granted that a canonical proof of a sentence must be unique up to certain minor syntactical details (such as, e.g., change of bound variables). When…