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A new heap game

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Aviezri S. Fraenkel, Dmitri Zusman

Combinatorics · Submitted 15 Sep 1998

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

The authors' main claim We analyse this extension of Wythoff's game and provide a polynomial-time strategy for it.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/9809075 (version 1)
Pith ID5JYZTUIQ, Pith's permanent record of this paper and its review
CitationAviezri S. Fraenkel, Dmitri Zusman. "A new heap game." arXiv:math/9809075 (1998). https://pith.science/paper/5JYZTUIQ
Claim paper

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, 2,887 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.38 · compares with prior results 0.43 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Given $k\ge 3$ heaps of tokens. The moves of the 2-player game introduced here are to either take a positive number of tokens from at most $k-1$ heaps, or to remove the {\sl same} positive number of tokens from all the $k$ heaps. We analyse this extension of Wythoff's game and provide a polynomial-time strategy for it.

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 Given $k\ge 3$ heaps of tokens. background 0.94 0.07 0.01 unclear 0.67
s1 The moves of the 2-player game introduced here are to either take a positive number of tokens from at most $k-1$ heaps, or to remove the {\sl same} positive number of tokens from all the $k$ heaps. contribution 0.73 0.52 0.06 asserted 1.00
s2 We analyse this extension of Wythoff's game and provide a polynomial-time strategy for it. contribution 0.89 0.96 0.85 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.63 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

Given $k\ge 3$ heaps of tokens. The moves of the 2-player game introduced here are to either take a positive number of tokens from at most $k-1$ heaps, or to remove the {\sl same} positive number of tokens from all the $k$ heaps. We analyse this extension of Wythoff's game and provide a polynomial-time strategy for it.

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