The free spectra of varieties generated by idempotent semigroups

• Date: 2018
• Main Authors: Pluhar, Gabriella, Wood, Japheth
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: free spectra; semigroup; band; 20M05; 08B20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/811
• Journal Title: Algebra and Discrete Mathematics

We give an exact formula for the logarithm of the free spectra of band varieties. We show that the the logarithm of the size of a free algebra in a band variety  is \(\frac{4}{(k-3)!}n^{k-3}\log n-\frac{4}{(k-3)!}n^{k-3}\sum_{j=1}^{k-3}\frac{1}{j}+ O(n^{k-4}\log n)\), where \(k\) is a constant depen...