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Centerpole sets for colorings of Abelian groups

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Taras Banakh, Ostap Chervak

Combinatorics · Submitted 12 Mar 2010

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

The authors' main claim Given a topological group $G$ we calculate or evaluate the cardinal characteristic $c_k(G)$ (and $c_k^B(G)$) equal to the smallest cardinality of a $k$-centerpole subset $C\subset G$ for (Borel) colorings of $G$.

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arXiv ID1003.2588 (version 3)
Pith IDG7GVDWUB, Pith's permanent record of this paper and its review
CitationOstap Chervak, Taras Banakh. "Centerpole sets for colorings of Abelian groups." arXiv:1003.2588 (2010). https://pith.science/paper/G7GVDWUB
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,540 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Given a topological group $G$ we calculate or evaluate the cardinal characteristic $c_k(G)$ (and $c_k^B(G)$) equal to the smallest cardinality of a $k$-centerpole subset $C\subset G$ for (Borel) colorings of $G$. A subset $C\subset G$ of a topological group $G$ is called {\em $k$-centerpole} if for each (Borel) $k$-coloring of $G$ there is an unbounded monochromatic subset $G$, which is symmetric with respect to a point $c\in C$ in the sense that $S=cS^{-1}c$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Given a topological group $G$ we calculate or evaluate the cardinal characteristic $c_k(G)$ (and $c_k^B(G)$) equal to the smallest cardinality of a $k$-centerpole subset $C\subset G$ for (Borel) colorings of $G$. contribution 0.86 0.87 0.27 asserted 1.00
s1 A subset $C\subset G$ of a topological group $G$ is called {\em $k$-centerpole} if for each (Borel) $k$-coloring of $G$ there is an unbounded monochromatic subset $G$, which is symmetric with respect to a point $c\in C$ in the sense that $S=cS^{-1}c$. background 0.97 0.10 0.05 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • 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

Given a topological group $G$ we calculate or evaluate the cardinal characteristic $c_k(G)$ (and $c_k^B(G)$) equal to the smallest cardinality of a $k$-centerpole subset $C\subset G$ for (Borel) colorings of $G$. A subset $C\subset G$ of a topological group $G$ is called {\em $k$-centerpole} if for each (Borel) $k$-coloring of $G$ there is an unbounded monochromatic subset $G$, which is symmetric with respect to a point $c\in C$ in the sense that $S=cS^{-1}c$.

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