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A refined multiplication formula for cluster characters

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Bernhard Keller, Pierre-Guy Plamondon, Fan Qin

Representation Theory · Submitted 3 Jan 2023

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

The authors' main claim We obtain a multiplication formula for cluster characters on (stably) 2-Calabi-Yau (Frobenius or) triangulated categories.

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arXiv ID2301.01059 (version 2)
Pith IDHUEP3AZA, Pith's permanent record of this paper and its review
CitationBernhard Keller, Fan Qin, Pierre-Guy Plamondon. "A refined multiplication formula for cluster characters." arXiv:2301.01059 (2023). https://pith.science/paper/HUEP3AZA
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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, 3,550 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We obtain a multiplication formula for cluster characters on (stably) 2-Calabi-Yau (Frobenius or) triangulated categories. This formula generalizes those known for arbitrary pairs of objects and for Auslander-Reiten triangles. As an application, we show that for cluster algebras of acyclic types, specialization of a cluster variable to 1 sends all cluster variables to elements of a cluster algebra of smaller rank. We also obtain application to the reduction of friezes of acyclic type.

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 We obtain a multiplication formula for cluster characters on (stably) 2-Calabi-Yau (Frobenius or) triangulated categories. contribution 0.68 0.96 0.87 asserted 1.00
s1 This formula generalizes those known for arbitrary pairs of objects and for Auslander-Reiten triangles. contribution 0.39 0.53 0.12 asserted 1.00
s2 As an application, we show that for cluster algebras of acyclic types, specialization of a cluster variable to 1 sends all cluster variables to elements of a cluster algebra of smaller rank. result 0.97 0.95 0.15 asserted 1.00
s3 We also obtain application to the reduction of friezes of acyclic type. result 0.56 0.94 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.

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not examined
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  • figures and tables
  • references and citing sentences
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  • 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

We obtain a multiplication formula for cluster characters on (stably) 2-Calabi-Yau (Frobenius or) triangulated categories. This formula generalizes those known for arbitrary pairs of objects and for Auslander-Reiten triangles. As an application, we show that for cluster algebras of acyclic types, specialization of a cluster variable to 1 sends all cluster variables to elements of a cluster algebra of smaller rank. We also obtain application to the reduction of friezes of acyclic type.

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References
How the literature uses it

2 arXiv papers cite this in 5 sentences

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 · 4 sentences without a confident label

Cites it as background 1 paper
  • Keller-Plamondon-Qin in [ref] obtained a refined multiplication formula for cluster characters of any 2-Calabi-Yau triangulated categories with a cluster tilting object. let $T$ be a cluster tilting object in $$.

    Motivic cluster multiplication formulas in 2-Calabi-Yau categories · The refined motivic weighted multiplication formula · 0.81

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