论文标题
负基础中的自动序列和Shevevev的某些猜想的证据
Automatic Sequences in Negative Bases and Proofs of Some Conjectures of Shevelev
论文作者
论文摘要
我们讨论自动序列中负基碱的使用。最近，已扩展了定理核心核桃，以允许使用碱（-k）表达变量，从而允许对z而不是n进行定量。这使我们能够证明对双面（BI-INFINITE）自动序列的结果。我们首先解释了核桃中负基础背后的理论。接下来，我们使用这种新版本的核桃来提供一个非常简单的证明，证明了Sheevelev定理的增强版本。我们利用我们的想法解决了2017年Shevelev的两个开放问题。我们还谴责了2000年涉及双限时二进制单词的Shur的结果。
We discuss the use of negative bases in automatic sequences. Recently the theorem-prover Walnut has been extended to allow the use of base (-k) to express variables, thus permitting quantification over Z instead of N. This enables us to prove results about two-sided (bi-infinite) automatic sequences. We first explain the theory behind negative bases in Walnut. Next, we use this new version of Walnut to give a very simple proof of a strengthened version of a theorem of Shevelev. We use our ideas to resolve two open problems of Shevelev from 2017. We also reprove a 2000 result of Shur involving bi-infinite binary words.
