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Generalized Commutative Association Schemes, Hypergroups, and Positive Product Formulas

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Michael Voit

Group Theory · Submitted 3 Aug 2017

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

The authors' main claim We show that discrete commutative hypergroups associated with such generalized association schemes admit dual positive convolutions at least on the support of the Plancherel measure.

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arXiv ID1708.01172 (version 1)
Pith IDVCR7EMWL, Pith's permanent record of this paper and its review
CitationMichael Voit. "Generalized Commutative Association Schemes, Hypergroups, and Positive Product Formulas." arXiv:1708.01172 (2017). https://pith.science/paper/VCR7EMWL
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,629 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.74 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.66 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

It is well known that finite commutative association schemes in the sense of the monograph of Bannai and Ito lead to finite commutative hypergroups with positive dual convolutions and even dual hypergroup structures. In this paper we present several discrete generalizations of association schemes which also lead to associated hypergroups. We show that discrete commutative hypergroups associated with such generalized association schemes admit dual positive convolutions at least on the support of the Plancherel measure. We hope that examples for this theory will lead to the existence of new dual positive product formulas in near future.

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 It is well known that finite commutative association schemes in the sense of the monograph of Bannai and Ito lead to finite commutative hypergroups with positive dual convolutions and even dual hypergroup structures. background 1.00 0.03 0.05 asserted 1.00
s1 In this paper we present several discrete generalizations of association schemes which also lead to associated hypergroups. contribution 1.00 0.88 0.17 asserted 1.00
s2 We show that discrete commutative hypergroups associated with such generalized association schemes admit dual positive convolutions at least on the support of the Plancherel measure. result 0.99 0.94 0.63 asserted 0.99
s3 We hope that examples for this theory will lead to the existence of new dual positive product formulas in near future. future work 1.00 0.05 0.06 speculative 0.60

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

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  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
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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

It is well known that finite commutative association schemes in the sense of the monograph of Bannai and Ito lead to finite commutative hypergroups with positive dual convolutions and even dual hypergroup structures. In this paper we present several discrete generalizations of association schemes which also lead to associated hypergroups. We show that discrete commutative hypergroups associated with such generalized association schemes admit dual positive convolutions at least on the support of the Plancherel measure. We hope that examples for this theory will lead to the existence of new dual positive product formulas in near future.

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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

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