What Is a Dehn Function?
نویسندگان
چکیده
1.1. Jigsaw puzzles reimagined. I will describe jigsaw puzzles that are somewhat different to the familiar kind. A box, shown in Figure 1, contains an infinite supply of the three types of pieces pictured on its side: one five–sided and two four–sided, their edges coloured green, blue and red and directed by arrows. It also holds an infinite supply of red, green and blue rods, again directed by arrows.
منابع مشابه
On Dehn Functions of Infinite Presentations of Groups
We introduce two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function) for infinite group presentations and prove the fundamental equivalence between the solvability of the word problem for a group presentation defined by a decidable set of defining words and the property of being computable for one of the newly introduced functions (this ...
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We study the Dehn functions of amalgamations, introducing the notion of strongly undistorted subgroups. Using this, we give conditions under which taking an amalgamation does not increase the Dehn function, generalizing one aspect of the combination theorem of Bestvina and Feighn. To obtain examples of strongly undistorted subgroups, we define and study the relative Dehn function of pairs of gr...
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For each automatic monoid the word problem can be solved in quadratic time (Campbell et al 1996), and hence, the Dehn function of a nitely presented automatic monoid is recursive. Here we show that this result on the Dehn function cannot be improved in general by presenting nitely presented bi-automatic monoids the Dehn functions of which realize arbitrary complexity classes that are suuciently...
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While Dehn functions, D(n), of finitely presented groups are very well studied in the literature, mean Dehn functions are much less considered. M. Gromov introduced the notion of mean Dehn function of a group, Dmean(n), suggesting that in many cases it should grow much more slowly than the Dehn function itself. Using only elementary counting methods, this paper presents some computations pointi...
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