代数的共生函数及其数学间隙
On cogrowth function of algebras and its logarithmical gap
摘要：
设$A \cong k\langle X \rangle / I$是一个结合代数.一个字母表上的有限字$X$是$I$ { \it -reducable}，如果它在$A$中的图像是长度-词典学上较小的字的$k$ -线性组合。子字最小$I$可约字中的{ \it阻塞}。{ \em共生}函数是长度为$\le n$的障碍物的数量。我们证明了一个非线性代数的共生函数要么是有界的，要么至少是代数的。我们还表明，一个一致经常性的字至少有数学共生。
英文摘要：
Let $A \cong k\langle X \rangle / I$ be an associative algebra. A finite word over alphabet $X$ is $I${\it-reducible} if its image in $A$ is a $k$-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal $I$-reducible word. A {\em cogrowth} function is number of obstructions of length $\le n$. We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
