论文标题
签名的二项式和申请Carnevale-Voll猜想的明确渐近造
Explicit Asymptotics for Signed Binomial Sums and Applications to Carnevale-Voll Conjecture
论文作者
论文摘要
卡内维尔（Carnevale）和沃尔（Voll）猜想J（-1）J $λ$ 1 J $λ$ 2 J = 0当$λ$ 1和$λ$ 2是两个不同的整数。当$λ$ 2或$λ$ 1- $λ$ 2很小时，我们会检查猜想。当比率为r：= $λ$ 1 /$λ$ 2的比率r：$λ$ 2时，我们调查其总和的渐近行为。我们找到一个明确的范围R $ \ ge $ 5.8362，该范围是True。我们表明，对于任何固定的R，猜想几乎是正确的。对于接近1的r，我们给出了几个明确的间隔，这些间隔也是如此。
Carnevale and Voll conjectured that j (--1) j $λ$ 1 j $λ$ 2 j = 0 when $λ$ 1 and $λ$ 2 are two distinct integers. We check the conjecture when either $λ$ 2 or $λ$ 1 -- $λ$ 2 is small. We investigate the asymptotic behaviour of their sum when the ratio r := $λ$ 1 /$λ$ 2 is fixed and $λ$ 2 goes to infinity. We find an explicit range r $\ge$ 5.8362 on which the conjecture is true. We show that the conjecture is almost surely true for any fixed r. For r close to 1, we give several explicit intervals on which the conjecture is also true.
