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Polynomial-time sortable stacks of burnt pancakes

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Anthony Labarre, Josef Cibulka

Data Structures and Algorithms · Submitted 1 Oct 2010

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

The authors' main claim In this work, we prove a new lower bound for sorting burnt pancakes, and show that an important class of permutations, known as "simple permutations", can be optimally sorted in polynomial time.

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arXiv ID1010.0219 (version 1)
Pith ID7OBX63TN, Pith's permanent record of this paper and its review
CitationAnthony Labarre, Josef Cibulka. "Polynomial-time sortable stacks of burnt pancakes." arXiv:1010.0219 (2010). https://pith.science/paper/7OBX63TN
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,299 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.33 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.45 · compares with prior results 0.21 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Pancake flipping, a famous open problem in computer science, can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible. In that context, a prefix reversal of length k reverses the order of the first k elements of the permutation. The burnt variant of pancake flipping involves permutations of signed integers, and reversals in that case not only reverse the order of elements but also invert their signs. Although three decades have now passed since the first works on these problems, neither their computational complexity nor the maximal number of prefix reversals needed to sort a permutation is yet known. In this work, we prove a new lower bound for sorting burnt pancakes, and show that an important class of permutations, known as "simple permutations", can be optimally sorted in polynomial time.

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 Pancake flipping, a famous open problem in computer science, can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible. background 1.00 0.05 0.03 asserted 0.94
s1 In that context, a prefix reversal of length k reverses the order of the first k elements of the permutation. background 1.00 0.07 0.02 asserted 1.00
s2 The burnt variant of pancake flipping involves permutations of signed integers, and reversals in that case not only reverse the order of elements but also invert their signs. background 1.00 0.05 0.02 asserted 1.00
s3 Although three decades have now passed since the first works on these problems, neither their computational complexity nor the maximal number of prefix reversals needed to sort a permutation is yet known. gap 0.99 0.04 0.03 asserted 1.00
s4 In this work, we prove a new lower bound for sorting burnt pancakes, and show that an important class of permutations, known as "simple permutations", can be optimally sorted in polynomial time. contribution 0.80 0.97 0.96 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

Pancake flipping, a famous open problem in computer science, can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible. In that context, a prefix reversal of length k reverses the order of the first k elements of the permutation. The burnt variant of pancake flipping involves permutations of signed integers, and reversals in that case not only reverse the order of elements but also invert their signs. Although three decades have now passed since the first works on these problems, neither their computational complexity nor the maximal number of prefix reversals needed to sort a permutation is yet known. In this work, we prove a new lower bound for sorting burnt pancakes, and show that an important class of permutations, known as "simple permutations", can be optimally sorted in polynomial time.

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