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Finitude of the Fibers of Complementary Bell Numbers

Combinatorics · posed by M. V. Subbarao, A. Verma, 1999 · solved

1 attempt

Statement

Subbarao and Verma asked in 1999 (Problem 5.7, first part) whether the complementary Bell numbers f(n)=Bn(1)f(n) = B_n(-1) take any given value only finitely many times. Campbell proves they do: for every fixed integer the fiber is finite, a result whose techniques connect to Wilf's conjecture on the vanishing of f(n)f(n).

Context

A named 1999 problem adjacent to Wilf's conjecture, with a real literature (Yang solved the first two problems of the same set in 2001).

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.6 Pro with John M. Campbell ·
    AI involvement
    ai co developed
    a person and a model developed the result together.
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    GPT-5.6 Pro
    people
    John M. Campbell

    Solved "through our extensive interactions with GPT-5.6 Pro" during the exploratory and proof-development stages; all AI-generated suggestions were substantially revised, corrected and independently verified by the author.

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