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There are More Than 2**(n/17) n-Letter Ternary Square-Free Words

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Doron Zeilberger (Temple University)

Combinatorics · Submitted 23 Sep 1998

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

The authors' main claim We prove that the `connective constant' for ternary square-free words is at least $2^{1/17} = 1.0416 ...

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arXiv IDmath/9809135 (version 1)
Pith IDLVGAP3D4, Pith's permanent record of this paper and its review
CitationDoron Zeilberger (Temple University). "There are More Than 2**(n/17) n-Letter Ternary Square-Free Words." arXiv:math/9809135 (1998). https://pith.science/paper/LVGAP3D4
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The compiled record

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, 2,947 input tokens.

What the abstract itself states, as probabilities: claims first 0.84 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We prove that the `connective constant' for ternary square-free words is at least $2^{1/17} = 1.0416 ... $, improving on Brinkhuis and Brandenburg's lower bounds of $2^{1/24}=1.0293 ...$ and $2^{1/22}=1.032 ...$ respectively. This is the first improvement since 1983.

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 prove that the `connective constant' for ternary square-free words is at least $2^{1/17} = 1.0416 ... result 0.95 0.96 0.89 asserted 1.00
s1 $, improving on Brinkhuis and Brandenburg's lower bounds of $2^{1/24}=1.0293 ...$ and $2^{1/22}=1.032 ...$ respectively. result 0.59 0.41 0.15 asserted 0.98
s2 This is the first improvement since 1983. interpretation 0.36 0.47 0.05 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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  • 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

We prove that the `connective constant' for ternary square-free words is at least $2^{1/17} = 1.0416 ... $, improving on Brinkhuis and Brandenburg's lower bounds of $2^{1/24}=1.0293 ...$ and $2^{1/22}=1.032 ...$ respectively. This is the first improvement since 1983.

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