Asymptotic growth of free spectra of band monoids
S Seif, J Wood - Semigroup Forum, 2007 - Springer
S Seif, J Wood
Semigroup Forum, 2007•SpringerFor a positive integer k≧3, the finite band monoid \bfB_k, a subdirectly irreducible band
monoid defined by JA Gerhard, it is shown for (f_n^\scriptsize\bfB_\tiny\bfk), the free
spectrum of the variety generated by \bfB_k, that (\log(f_n^\scriptsize\bfB_\tiny\bfk)) is in the
asymptotic class of n^k-1\logn, thereby answering in the negative a question in" 64
Problems in Universal Algebra" from the 2001 Budapest conference, A Course in Tame
Congruence Theory.
monoid defined by JA Gerhard, it is shown for (f_n^\scriptsize\bfB_\tiny\bfk), the free
spectrum of the variety generated by \bfB_k, that (\log(f_n^\scriptsize\bfB_\tiny\bfk)) is in the
asymptotic class of n^k-1\logn, thereby answering in the negative a question in" 64
Problems in Universal Algebra" from the 2001 Budapest conference, A Course in Tame
Congruence Theory.
Abstract
For a positive integer , the finite band monoid , a subdirectly irreducible band monoid defined by J.A. Gerhard, it is shown for $(f_n^{\mbox{\scriptsize\bf B}_{\mbox{\tiny\bf k}}})$, the free spectrum of the variety generated by , that $(\log(f_n^{\mbox{\scriptsize\bf B}_{\mbox{\tiny\bf k}}}))$ is in the asymptotic class of , thereby answering in the negative a question in "64 Problems in Universal Algebra" from the 2001 Budapest conference, A Course in Tame Congruence Theory.
Springer
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