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
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
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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
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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
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A tropical curve is a graph with specified edge lengths, some of which may be infinite. Various facts and attributes about algebraic curves have analogs for tropical curves. In this article, we focus on divisors and linear series, and prove the Riemann-Roch formula for divisors …
Mathematics / Algebraic geometry
