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Divisors on complete multigraphs and Donaldson-Thomas invariants of loop quivers

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Matjaž Konvalinka, Markus Reineke, Vasu Tewari

Combinatorics · Submitted 13 Nov 2021

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

The authors' main claim We provide an alternative characterization for these divisors, by virtue of which we show that orbits of this action are enumerated by the numerical Donaldson-Thomas invariants of $(m+1)$-loop quivers.

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arXiv ID2111.07071 (version 1)
Pith ID3JWRHVRK, Pith's permanent record of this paper and its review
CitationMarkus Reineke, Matja\v{z} Konvalinka, Vasu Tewari. "Divisors on complete multigraphs and Donaldson-Thomas invariants of loop quivers." arXiv:2111.07071 (2021). https://pith.science/paper/3JWRHVRK
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,043 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.37 · compares with prior results 0.14 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study the action of $S_n$ on the set of break divisors on complete multigraphs $K_{n}^m$. We provide an alternative characterization for these divisors, by virtue of which we show that orbits of this action are enumerated by the numerical Donaldson-Thomas invariants of $(m+1)$-loop quivers. Our characterization also allows us to restrict this action to $S_{n-1}$ and we identify the resulting $S_{n-1}$-module as that afforded by $K_n^m$-parking functions.

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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 study the action of $S_n$ on the set of break divisors on complete multigraphs $K_{n}^m$. contribution 0.92 0.90 0.05 asserted 0.89
s1 We provide an alternative characterization for these divisors, by virtue of which we show that orbits of this action are enumerated by the numerical Donaldson-Thomas invariants of $(m+1)$-loop quivers. result 0.92 0.94 0.76 asserted 1.00
s2 Our characterization also allows us to restrict this action to $S_{n-1}$ and we identify the resulting $S_{n-1}$-module as that afforded by $K_n^m$-parking functions. result 0.93 0.95 0.17 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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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 study the action of $S_n$ on the set of break divisors on complete multigraphs $K_{n}^m$. We provide an alternative characterization for these divisors, by virtue of which we show that orbits of this action are enumerated by the numerical Donaldson-Thomas invariants of $(m+1)$-loop quivers. Our characterization also allows us to restrict this action to $S_{n-1}$ and we identify the resulting $S_{n-1}$-module as that afforded by $K_n^m$-parking functions.

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