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On a Family of Conjectures of Joel Lewis on Alternating Permutations

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Miklos Bona

Combinatorics · Submitted 8 May 2012

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

The authors' main claim We prove generalized versions of some conjectures of Joel Lewis on the number of alternating permutations avoiding certain patterns.

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arXiv ID1205.1778 (version 1)
Pith IDMN6LULSD, Pith's permanent record of this paper and its review
CitationMiklos Bona. "On a Family of Conjectures of Joel Lewis on Alternating Permutations." arXiv:1205.1778 (2012). https://pith.science/paper/MN6LULSD
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,225 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.29 · 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 generalized versions of some conjectures of Joel Lewis on the number of alternating permutations avoiding certain patterns. Our main tool is the perhaps surprising observation that a classic bijection on pattern avoiding permutations often preserves the alternating property.

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 generalized versions of some conjectures of Joel Lewis on the number of alternating permutations avoiding certain patterns. contribution 0.85 0.96 0.91 asserted 1.00
s1 Our main tool is the perhaps surprising observation that a classic bijection on pattern avoiding permutations often preserves the alternating property. method 0.97 0.84 0.10 asserted 0.94

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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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 generalized versions of some conjectures of Joel Lewis on the number of alternating permutations avoiding certain patterns. Our main tool is the perhaps surprising observation that a classic bijection on pattern avoiding permutations often preserves the alternating property.

Human review

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How the literature uses it

1 arXiv paper cite this in 3 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

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