Geodesic
The free spectra of varieties generated by idempotent semigroups
Algebra and discrete mathematics, no. 2 (2008), pp. 89-100 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 depending on the variety.
Keywords: free spectra, semigroup, band. 
@article{ADM_2008_2_a5,
     author = {Gabriella Pluh\'ar and Japheth Wood},
     title = {The free spectra of varieties generated by idempotent semigroups},
     journal = {Algebra and discrete mathematics},
     pages = {89--100},
     year = {2008},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2008_2_a5/}
}
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Gabriella Pluhár; Japheth Wood. The free spectra of varieties generated by idempotent semigroups. Algebra and discrete mathematics, no. 2 (2008), pp. 89-100. http://geodesic.mathdoc.fr/item/ADM_2008_2_a5/