We study proportions of consecutive occurrences of permutations of a given size. Specifically, the limit of such proportions on large permutations forms a region, called feasible region. We show that this feasible region is a polytope, more precisely the cycle polytope of a specific graph called overlap graph. This allows us to compute the dimension, vertices and faces of the polytope, and to determine the equations that define it. Finally we prove that the limit of classical occurrences and consecutive occurrences are in some sense independent. As a consequence, the scaling limit of a sequence of permutations induces no constraints on the local limit and vice versa.
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Accepted:
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Keywords: Permutation patterns, cycle polytopes, overlap graphs.
Borga, Jacopo 1; Penaguiao, Raul 1
CC-BY 4.0
@article{ALCO_2020__3_6_1259_0,
author = {Borga, Jacopo and Penaguiao, Raul},
title = {The feasible region for consecutive patterns of permutations is a cycle polytope},
journal = {Algebraic Combinatorics},
pages = {1259--1281},
publisher = {MathOA foundation},
volume = {3},
number = {6},
year = {2020},
doi = {10.5802/alco.135},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.135/}
}
TY - JOUR AU - Borga, Jacopo AU - Penaguiao, Raul TI - The feasible region for consecutive patterns of permutations is a cycle polytope JO - Algebraic Combinatorics PY - 2020 SP - 1259 EP - 1281 VL - 3 IS - 6 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.135/ DO - 10.5802/alco.135 LA - en ID - ALCO_2020__3_6_1259_0 ER -
%0 Journal Article %A Borga, Jacopo %A Penaguiao, Raul %T The feasible region for consecutive patterns of permutations is a cycle polytope %J Algebraic Combinatorics %D 2020 %P 1259-1281 %V 3 %N 6 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.135/ %R 10.5802/alco.135 %G en %F ALCO_2020__3_6_1259_0
Borga, Jacopo; Penaguiao, Raul. The feasible region for consecutive patterns of permutations is a cycle polytope. Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1259-1281. doi : 10.5802/alco.135. https://alco.centre-mersenne.org/articles/10.5802/alco.135/
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