152 research outputs found
The Growth of Grigorchuk's Group
In 1980 Rostislav Grigorchuk constructed a group of intermediate growth,
and later obtained the following estimates on its growth function:
where
. Using elementary methods we bring the upper
bound down to , where is
the real root of the polynomial
Lamps, Factorizations and Finite Fields
I answer a question from the 1993 International Mathematical Olympiads by
constructing an equivalent algebraic problem, and unearth a surprising
behaviour of some polynomials over the two-element field.Comment: 6 pages, elementary conten
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