In the paper, we study equations in one variable over free semilattices. We show that the average number of solutions of a random equation over a free semilattice of 3n + 2 • 2n a rank n is equal to - -. It is proved that the average number of irreducible components of algebraic sets defined by equations over a free semilattice of a countable rank is equal to 1.
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- Title Random equations over free semilattices
- Headline Random equations over free semilattices
- Publesher
Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 36
- Date:
- DOI 10.17223/20710410/36/1
Keywords
свободная полурешётка, уравнение, неприводимые компоненты, free semilattice, equation, irreducible componentsAuthors
References
Oilman R., Myasnikov A., and Roman'kov V. Random equations in nilpotent groups // J. Algebra. 2012. V.352. No. 1. P. 192-214.
Oilman R., Myasnikov A., and Roman'kov V. Random equations in free groups // Groups Complexity Cryptol. 2011. V. 3. No. 2. P. 257-284.
Roman'kov V. Equations over groups // Groups Complexity Cryptol. 2012. V. 4. No. 2. P. 191-239.
Daniyarova E., Miasnikov A., and Remeslennikov V. Unification theorems in algebraic geometry // Algebra and Discrete Mathematics. Hackensack, 2008. P. 80-112.
Даниярова Э. Ю., Мясников А. Г., Ремесленников В. Н Алгебраическая геометрия над алгебраическими системами. II. Основания // Фундамент. и прикл. матем. 2012. Т. 17. №1. С.65-106.
Шевляков А. Н. Эквивалентные уравнения над полурешетками // Сиб. электрон. матем. изв. 2016. Т. 13. С. 478-490.
Шевляков А. Н. Элементы алгебраической геометрии над свободной полурешеткой // Алгебра и логика. 2015. Т. 54. №3. С. 399-420.
Random equations over free semilattices | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2017. № 36. DOI: 10.17223/20710410/36/1
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