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Three alternating sign matrix identities in search of bijective proofs

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arxiv math/0007114 v1 pith:44LMODF4 submitted 2000-07-18 math.CO math.HO

David M. Bressoud This is my paper · ORCID
classification math.COmath.HO
keywords identitiesknownproofsthreealternatingbijectivesigncombinatorial
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This paper highlights three known identities, each of which involves sums over alternating sign matrices. While proofs of all three are known, the only known derivations are as corollaries of difficult results. The simplicity and natural combinatorial interpretation of these identities, however, suggest that there should be direct, bijective proofs.

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    math.HO 2025-06 conditional novelty 6.0 of 10

    An LLM-assisted corpus study finds that roughly 3% to 12% of 5,000 arXiv math papers contain clear or borderline appeals to mathematical explanation, with frequency varying by subfield.

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