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@article{1646924, author = {Kenyon, Richard and Kráľ, Daniel and Radin, Charles and Winkler, Peter}, article_location = {HOBOKEN}, article_number = {1}, doi = {http://dx.doi.org/10.1002/rsa.20882}, keywords = {graphons; permutation patterns; permutons}, language = {eng}, issn = {1042-9832}, journal = {Random Structures and Algorithms}, title = {Permutations with fixed pattern densities}, url = {http://dx.doi.org/10.1002/rsa.20882}, volume = {56}, year = {2020} }
TY - JOUR ID - 1646924 AU - Kenyon, Richard - Kráľ, Daniel - Radin, Charles - Winkler, Peter PY - 2020 TI - Permutations with fixed pattern densities JF - Random Structures and Algorithms VL - 56 IS - 1 SP - 220-250 EP - 220-250 PB - WILEY SN - 10429832 KW - graphons KW - permutation patterns KW - permutons UR - http://dx.doi.org/10.1002/rsa.20882 L2 - http://dx.doi.org/10.1002/rsa.20882 N2 - We study scaling limits of random permutations ("permutons") constrained by having fixed densities of a finite number of patterns. We show that the limit shapes are determined by maximizing entropy over permutons with those constraints. In particular, we compute (exactly or numerically) the limit shapes with fixed 12 density, with fixed 12 and 123 densities, with fixed 12 density and the sum of 123 and 213 densities, and with fixed 123 and 321 densities. In the last case we explore a particular phase transition. To obtain our results, we also provide a description of permutons using a dynamic construction. ER -
KENYON, Richard, Daniel KRÁĽ, Charles RADIN and Peter WINKLER. Permutations with fixed pattern densities. \textit{Random Structures and Algorithms}. HOBOKEN: WILEY, 2020, vol.~56, No~1, p.~220-250. ISSN~1042-9832. Available from: https://dx.doi.org/10.1002/rsa.20882.
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