What is Expositio?
A public repository for expository academic papers, with an integrated scholarly record.
Expositio is a place to read and cite expository work. Papers are published as stable,
citable records, while remaining connected to later versions, editorial decisions,
and related context.
Some papers are early drafts; others have been peer reviewed or formally published.
Each paper remains readable on its own, while preserving the history behind it.
The result is both a reading room and a record: a place to browse by field, read
papers in stable form, and follow their development over time.
v1
Sidorenko's conjecture predicts that the homomorphism density of a bipartite graph H in a host graph G satisfies t_H(G) ≥ t_{K_2}(G)^|E(H)|. We introduce the conjecture through homomorphism densities, prove the finite-host inequality for P_3, C_4, and the complete bipartite grap…
Mathematics / Combinatorics
v1
In this paper we show that the chromatic function $P(G,t)$ is always a polynomial. We then ask a simple question: where does this polynomial equal zero? Tutte showed that two stretches of the real line, $(-\infty,0)$ and $(0,1)$, can never contain a root. Jackson showed in 1993 …
Mathematics / Combinatorics
v1
This paper primarily discusses the proof of the Mahler-Lech-Skolem through the uses of p-adic analysis in its connection to Strassman's Theorem and p-adic interpolation. As this theorem is so closely related to p-adic analysis, we make a brief mention of the core concepts in p-a…
Mathematics / Sequences, series, summability
v1
Combinatorial game theory and coding theory appear to be completely separate fields at first glance. However, they share a profound connection through structures known as lexicographic codes, or lexicodes. First introduced by Conway and Sloane in 1986, lexicodes are generated by…
Mathematics / Combinatorics
v1
Hyperbolic geometry is a non-Euclidean geometry where geodesics play the role of straight lines. It is characterised by a constant negative curvature. The idea was conceived when mathematicians tried to understand the parallel postulate. This expository paper develops the founda…
Mathematics / Differential geometry
Mathematics / Geometry
Mathematics / Topological groups, Lie groups
Mathematics / Functions of a complex variable
v1
In statistics, signal processing, and machine learning, the information we want from a matrix is carried by its singular values and singular vectors, yet the matrix we observe is almost never the one we want: it has been corrupted by measurement error, finite-sample fluctuation,…
Mathematics / Linear and multilinear algebra; matrix theory
