Asymptotic distribution of fixed points of pattern-avoiding involutions
For a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In particular we consider monotone patterns of arbitrary length as well as all patterns of length 3. For monotone patterns we ut...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2017-12-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3658/pdf |
| _version_ | 1797270073097846784 |
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| author | Samuel Miner Douglas Rizzolo Erik Slivken |
| author_facet | Samuel Miner Douglas Rizzolo Erik Slivken |
| author_sort | Samuel Miner |
| collection | DOAJ |
| description | For a variety of pattern-avoiding classes, we describe the limiting
distribution for the number of fixed points for involutions chosen uniformly at
random from that class. In particular we consider monotone patterns of
arbitrary length as well as all patterns of length 3. For monotone patterns we
utilize the connection with standard Young tableaux with at most $k$ rows and
involutions avoiding a monotone pattern of length $k$. For every pattern of
length 3 we give the bivariate generating function with respect to fixed points
for the involutions that avoid that pattern, and where applicable apply tools
from analytic combinatorics to extract information about the limiting
distribution from the generating function. Many well-known distributions
appear. |
| first_indexed | 2024-04-25T01:58:28Z |
| format | Article |
| id | doaj.art-5c6cad455a3b41c49c1cd9328b250ec1 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:58:28Z |
| publishDate | 2017-12-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-5c6cad455a3b41c49c1cd9328b250ec12024-03-07T15:33:33ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502017-12-01Vol. 19 no. 2, Permutation...Permutation Patterns10.23638/DMTCS-19-2-53658Asymptotic distribution of fixed points of pattern-avoiding involutionsSamuel MinerDouglas RizzoloErik SlivkenFor a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In particular we consider monotone patterns of arbitrary length as well as all patterns of length 3. For monotone patterns we utilize the connection with standard Young tableaux with at most $k$ rows and involutions avoiding a monotone pattern of length $k$. For every pattern of length 3 we give the bivariate generating function with respect to fixed points for the involutions that avoid that pattern, and where applicable apply tools from analytic combinatorics to extract information about the limiting distribution from the generating function. Many well-known distributions appear.https://dmtcs.episciences.org/3658/pdfmathematics - combinatoricsmathematics - probability60c05 |
| spellingShingle | Samuel Miner Douglas Rizzolo Erik Slivken Asymptotic distribution of fixed points of pattern-avoiding involutions Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics mathematics - probability 60c05 |
| title | Asymptotic distribution of fixed points of pattern-avoiding involutions |
| title_full | Asymptotic distribution of fixed points of pattern-avoiding involutions |
| title_fullStr | Asymptotic distribution of fixed points of pattern-avoiding involutions |
| title_full_unstemmed | Asymptotic distribution of fixed points of pattern-avoiding involutions |
| title_short | Asymptotic distribution of fixed points of pattern-avoiding involutions |
| title_sort | asymptotic distribution of fixed points of pattern avoiding involutions |
| topic | mathematics - combinatorics mathematics - probability 60c05 |
| url | https://dmtcs.episciences.org/3658/pdf |
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