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Finitude of the Fibers of Complementary Bell Numbers

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

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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).

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    John M. Campbell, using GPT-5.6 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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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