广义$k$ -正则序列II：数字模式与超越
Generalized $k$-regular sequences II:digital pattern and transcendence
摘要：
本文证明了由数字模式序列生成的不可数实数量给出了超越数。这一结果给出了Morton和Mortant [MortM]中的主要定理的推广，该定理指出由数字模式序列生成的可数实数给出了超越数。我们的方法依赖于Adamczewski-Bugeaud [AdB 2]建立的组合定量超越准则和作者[Mi2]引入的广义$k$ -正则序列的性质。
英文摘要：
In this paper, we prove that an uncountable quantity of real numbers generated by digital pattern sequences gives the transcendental number. This result gives a generalization of Main theorem in Morton and Mourant [MortM], which state that countable real numbers generated by digital pattern sequences gives the transcendental number. Our method relies on the combinatorial quantitative transcendence criterion established by Adamczewski-Bugeaud [AdB2] and the properties of generalized $k$-regular sequences, which is introduced by the author [Mi2].
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