combinatorics / q-series and partitions
Han and Xiong extended the Gaussian binomial coefficient to positive rational index and conjectured that its integer trace, the integer-exponent part of the resulting power series, is coefficientwise largest at the integer point. Ono's paper proves a support-dominance theorem settling the conjecture for a large family of rational parameters and reduces the full conjecture to unit fractions, with a finite computer verification covering every remaining case up to a fixed bound.
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Settles the conjecture for a large family and reduces the rest to unit fractions; the general unit-fraction case remains open.
Research memory
Han and Xiong extended the Gaussian binomial coefficient to positive rational index and conjectured that its integer trace, the integer-exponent part of the resulting power series, is coefficientwise largest at the integer point. Ono's paper proves a support-dominance theorem settling the conjecture for a large family of rational parameters and reduces the full conjecture to unit fractions, with a finite computer verification covering every remaining case up to a fixed bound.
Settles the conjecture for a large family and reduces the rest to unit fractions; the general unit-fraction case remains open.
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