Algebraic matroids in action

Jessica Sidman; Louis Theran; Zvi Rosen

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Algebraic matroids in action

Zvi Rosen, Jessica Sidman, Louis Theran

Combinatorics · Submitted 4 Sep 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We give a self-contained introduction to algebraic matroids together with examples highlighting their potential application.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,647 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

In recent years, various notions of algebraic independence have emerged as a central and unifying theme in a number of areas of applied mathematics, including algebraic statistics and the rigidity theory of bar-and-joint frameworks. In each of these settings the fundamental problem is to determine the extent to which certain unknowns depend algebraically on given data. This has, in turn, led to a resurgence of interest in algebraic matroids, which are the combinatorial formalism for algebraic (in)dependence. We give a self-contained introduction to algebraic matroids together with examples highlighting their potential application.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In recent years, various notions of algebraic independence have emerged as a central and unifying theme in a number of areas of applied mathematics, including algebraic statistics and the rigidity theory of bar-and-joint frameworks.	background 1.00	0.04	0.04	asserted 1.00
s1	In each of these settings the fundamental problem is to determine the extent to which certain unknowns depend algebraically on given data.	background 1.00	0.05	0.03	asserted 1.00
s2	This has, in turn, led to a resurgence of interest in algebraic matroids, which are the combinatorial formalism for algebraic (in)dependence.	background 0.99	0.07	0.09	asserted 1.00
s3	We give a self-contained introduction to algebraic matroids together with examples highlighting their potential application.	contribution 1.00	0.93	0.22	asserted 0.98

What kind of paper the classifier reports this is: review 0.99 · evidence from argument 0.61.

What was examined, and what was not

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arXiv listing abstract v3

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full text
figures and tables
references and citing sentences
relations to other papers

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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

In recent years, various notions of algebraic independence have emerged as a central and unifying theme in a number of areas of applied mathematics, including algebraic statistics and the rigidity theory of bar-and-joint frameworks. In each of these settings the fundamental problem is to determine the extent to which certain unknowns depend algebraically on given data. This has, in turn, led to a resurgence of interest in algebraic matroids, which are the combinatorial formalism for algebraic (in)dependence. We give a self-contained introduction to algebraic matroids together with examples highlighting their potential application.

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1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper

There is also a way to naturally associate a matroid to a variety and some recent work has been done studying and applying such matroids [ref] .

Identifiability in Phylogenetics using Algebraic Matroids · Algebraic Matroids · 0.93

What it cites · 2 sentences without a confident label

Uses data or values from 1 paper

The dimension of $_d,n$ is $dn - d+12$ (see [ref] ), so no independent set $G$ in the algebraic matroid $(K_n,__d,n)$ can contain more than this many edges, since the dimension of $π_G$ is bounded by that of $_d,n$.

Point Configurations and Cayley-Menger Varieties · Distance geometry and rigidity theory · 0.90

Cites as support 1 paper

It follows from work of Whiteley [ref] and Saliola and Whiteley [ref] , that $I_n,d$ has a matroid isomorphic to the one associated with the ideal of the $(d+2)×(d+2)$ minors of a generic symmetric $n×n$ matrix, modulo its diagonal.

Some notes on the equivalence of first-order rigidity in various geometries · Distance geometry and rigidity theory · 0.97

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