A combinatorial proof establishes that the normalized Jacobi triple product tails have nonnegative coefficients in their bivariate generating function expansion, implying Merca's conjecture.
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math.CO 2years
2026 2verdicts
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Provides combinatorial interpretations of the bilateral truncated Jacobi triple product identity in terms of minimal excludant integers in partitions.
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A combinatorial proof for the positivity of the normalized Jacobi triple product tails
A combinatorial proof establishes that the normalized Jacobi triple product tails have nonnegative coefficients in their bivariate generating function expansion, implying Merca's conjecture.
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Minimal excludant integer and bilateral truncated Jacobi triple product identity
Provides combinatorial interpretations of the bilateral truncated Jacobi triple product identity in terms of minimal excludant integers in partitions.