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A classification of plane and planar 2-trees

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G. Labelle, C. Lamathe, P. Leroux

Combinatorics · Submitted 6 Feb 2002

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

The authors' main claim We then deduce the explicit molecular expansion of these species, i.e a classification of their structures according to their stabilizers.

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arXiv IDmath/0202052 (version 1)
Pith IDGPBSXXH7, Pith's permanent record of this paper and its review
CitationC. Lamathe, G. Labelle, P. Leroux. "A classification of plane and planar 2-trees." arXiv:math/0202052 (2002). https://pith.science/paper/GPBSXXH7
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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, 3,578 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.27 · 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 present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e a classification of their structures according to their stabilizers. There result explicit formulas in terms of Catalan numbers for their associated generating series, including the asymmetry index series. This work is closely related to the enumeration of polyene hydrocarbons of molecular formula C_nH_n+2.

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 present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. contribution 1.00 0.95 0.15 asserted 1.00
s1 We then deduce the explicit molecular expansion of these species, i.e a classification of their structures according to their stabilizers. contribution 0.51 0.96 0.39 asserted 1.00
s2 There result explicit formulas in terms of Catalan numbers for their associated generating series, including the asymmetry index series. result 1.00 0.93 0.39 asserted 1.00
s3 This work is closely related to the enumeration of polyene hydrocarbons of molecular formula C_nH_n+2. background 0.50 0.26 0.05 asserted 0.99

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
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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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 present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e a classification of their structures according to their stabilizers. There result explicit formulas in terms of Catalan numbers for their associated generating series, including the asymmetry index series. This work is closely related to the enumeration of polyene hydrocarbons of molecular formula C_nH_n+2.

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