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@inproceedings{2386887, author = {Garbe, Frederik and Kráľ, Daniel and Malekshahian, Alexandru and Penaguiao, Raul}, address = {Brno}, booktitle = {European Conference on Combinatorics, Graph Theory and Applications}, doi = {http://dx.doi.org/10.5817/CZ.MUNI.EUROCOMB23-065}, keywords = {permutations; permutation limits; patterns}, howpublished = {elektronická verze "online"}, language = {eng}, location = {Brno}, pages = {471-477}, publisher = {MUNI Press}, title = {The dimension of the feasible region of pattern densities}, url = {https://journals.muni.cz/eurocomb/article/view/35599}, year = {2023} }
TY - JOUR ID - 2386887 AU - Garbe, Frederik - Kráľ, Daniel - Malekshahian, Alexandru - Penaguiao, Raul PY - 2023 TI - The dimension of the feasible region of pattern densities PB - MUNI Press CY - Brno KW - permutations KW - permutation limits KW - patterns UR - https://journals.muni.cz/eurocomb/article/view/35599 N2 - A classical result of Erdős, Lovász and Spencer from the late 1970s asserts that the dimension of the feasible region of homomorphic densities of graphs with at most k vertices in large graphs is equal to the number of connected graphs with at most k vertices. Glebov et al. showed that pattern densities of indecomposable permutations are independent, i.e., the dimension of the feasible region of densities of k-patterns is at least the number of non-trivial indecomposable permutations of size at most k. We identify a larger set of permutations, which are called Lyndon permutations, whose pattern densities are independent, and show that the dimension of the feasible region of densities of k-patterns is equal to the number of non-trivial Lyndon permutations of size at most k. ER -
GARBE, Frederik, Daniel KRÁĽ, Alexandru MALEKSHAHIAN and Raul PENAGUIAO. The dimension of the feasible region of pattern densities. Online. In \textit{European Conference on Combinatorics, Graph Theory and Applications}. Brno: MUNI Press, 2023, p.~471-477. ISSN~2788-3116. Available from: https://dx.doi.org/10.5817/CZ.MUNI.EUROCOMB23-065.
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