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- W2898059104 abstract "We establish new results on the possible growth rates for the sequence (f_n) counting the number of orbits of a given oligomorphic group on unordered sets of size n. Macpherson showed that for primitive actions, the growth is at least exponential (if the sequence is not constant equal to 1). The best lower bound previously known for the base of the exponential was obtained by Merola. We establishing the optimal value of 2 in the case where the structure is unstable. This allows us to improve on Merola's bound and also obtain the optimal value for structures homogeneous in a finite relational language. Finally, we show that the study of sequences (f_n) of sub-exponential growth reduces to the omega-stable case." @default.
- W2898059104 created "2018-10-26" @default.
- W2898059104 creator A5071685293 @default.
- W2898059104 date "2018-10-15" @default.
- W2898059104 modified "2023-09-27" @default.
- W2898059104 title "On omega-categorical structures with few finite substructures" @default.
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