Equations in finite semigroups: Explicit enumeration and asymptotics of solution numbers (Q598458)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equations in finite semigroups: Explicit enumeration and asymptotics of solution numbers |
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Equations in finite semigroups: Explicit enumeration and asymptotics of solution numbers (English)
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6 August 2004
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The authors study the number of solutions of the equation \(X^\alpha = X^\beta\) in a finite semigroup \(G\), and also the number of solutions of the system \(X^2=X\), \(Y^2=Y\), \(XY=YX\) in \(H \wr T_n\), the wreath product of an arbitrary finite group \(H\) with the full transformation semigroup \(T_n\) on \(n\) letters. Both exact formulas and asymptotic estimates are given.
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equations in semigroups
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wreath products
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asymptotics of solution numbers
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Hayman asymptotics
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multinomial sum
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