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On the monoid of partial isometries of a wheel graph

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Vítor H. Fernandes

Rings and Algebras · Submitted 30 Jul 2023

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

The authors' main claim Our main objective is to determine the rank of $DPW_n$.

how it is stated · asserted 0.94 read the record →

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arXiv ID2307.16257 (version 2)
Pith IDQJOKBMNP, Pith's permanent record of this paper and its review
CitationV\'itor H. Fernandes. "On the monoid of partial isometries of a wheel graph." arXiv:2307.16257 (2023). https://pith.science/paper/QJOKBMNP
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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, 3,511 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this paper, we consider the monoid $DPW_n$ of all partial isometries of a wheel graph $W_n$ with $n+1$ vertices. Our main objective is to determine the rank of $DPW_n$. In the process, we also compute the ranks of three notable subsemigroups of $DPW_n$. We also describe Green's relations of $DPW_n$ and of its three considered subsemigroups.

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 In this paper, we consider the monoid $DPW_n$ of all partial isometries of a wheel graph $W_n$ with $n+1$ vertices. contribution 0.57 0.63 0.03 asserted 0.94
s1 Our main objective is to determine the rank of $DPW_n$. contribution 0.95 0.45 0.11 asserted 0.94
s2 In the process, we also compute the ranks of three notable subsemigroups of $DPW_n$. contribution 0.76 0.95 0.05 asserted 1.00
s3 We also describe Green's relations of $DPW_n$ and of its three considered subsemigroups. contribution 0.75 0.95 0.06 asserted 1.00

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

What was examined, and what was not

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  • figures and tables
  • references and citing sentences
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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 this paper, we consider the monoid $DPW_n$ of all partial isometries of a wheel graph $W_n$ with $n+1$ vertices. Our main objective is to determine the rank of $DPW_n$. In the process, we also compute the ranks of three notable subsemigroups of $DPW_n$. We also describe Green's relations of $DPW_n$ and of its three considered subsemigroups.

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