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Documents authored by Albert, Michael

Document
DOI: 10.4230/DagRep.8.11.1
Genomics, Pattern Avoidance, and Statistical Mechanics (Dagstuhl Seminar 18451)

Authors: Michael Albert, David Bevan, Miklós Bóna, and István Miklós

Published in: Dagstuhl Reports, Volume 8, Issue 11 (2019)

Abstract
We summarize key features of the workshop, such as the three main research areas in which the participants are active, the number and types of talks, and the geographic diversity of the attendees. We also provide a sampling of the collaborations started at the workshop, and explain why we believe that the workshop was successful, and why we believe it should take place again in the future.
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Michael Albert, David Bevan, Miklós Bóna, and István Miklós. Genomics, Pattern Avoidance, and Statistical Mechanics (Dagstuhl Seminar 18451). In Dagstuhl Reports, Volume 8, Issue 11, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Article{albert_et_al:DagRep.8.11.1,
  author =	{Albert, Michael and Bevan, David and B\'{o}na, Mikl\'{o}s and Mikl\'{o}s, Istv\'{a}n},
  title =	{{Genomics, Pattern Avoidance, and Statistical Mechanics (Dagstuhl Seminar 18451)}},
  pages =	{1--20},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2019},
  volume =	{8},
  number =	{11},
  editor =	{Albert, Michael and Bevan, David and B\'{o}na, Mikl\'{o}s and Mikl\'{o}s, Istv\'{a}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.8.11.1},
  URN =		{urn:nbn:de:0030-drops-103539},
  doi =		{10.4230/DagRep.8.11.1},
  annote =	{Keywords: Genome rearrangements, Matrix, Pattern, Permutation, Statistical Mechanics}
}
Document
DOI: 10.4230/LIPIcs.AofA.2018.9
Permutations in Binary Trees and Split Trees

Authors: Michael Albert, Cecilia Holmgren, Tony Johansson, and Fiona Skerman

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)

Abstract
We investigate the number of permutations that occur in random node labellings of trees. This is a generalisation of the number of subpermutations occuring in a random permutation. It also generalises some recent results on the number of inversions in randomly labelled trees [Cai et al., 2017]. We consider complete binary trees as well as random split trees a large class of random trees of logarithmic height introduced by Devroye [Devroye, 1998]. Split trees consist of nodes (bags) which can contain balls and are generated by a random trickle down process of balls through the nodes. For complete binary trees we show that asymptotically the cumulants of the number of occurrences of a fixed permutation in the random node labelling have explicit formulas. Our other main theorem is to show that for a random split tree with high probability the cumulants of the number of occurrences are asymptotically an explicit parameter of the split tree. For the proof of the second theorem we show some results on the number of embeddings of digraphs into split trees which may be of independent interest.
Cite as

Michael Albert, Cecilia Holmgren, Tony Johansson, and Fiona Skerman. Permutations in Binary Trees and Split Trees. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 9:1-9:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{albert_et_al:LIPIcs.AofA.2018.9,
  author =	{Albert, Michael and Holmgren, Cecilia and Johansson, Tony and Skerman, Fiona},
  title =	{{Permutations in Binary Trees and Split Trees}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{9:1--9:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.9},
  URN =		{urn:nbn:de:0030-drops-89025},
  doi =		{10.4230/LIPIcs.AofA.2018.9},
  annote =	{Keywords: random trees, split trees, permutations, inversions, cumulant}
}
Document
DOI: 10.4230/DagRep.6.2.65
Pattern Avoidance and Genome Sorting (Dagstuhl Seminar 16071)

Authors: Michael Albert, Miklós Bóna, István Miklós, and Einar Steingrimsson

Published in: Dagstuhl Reports, Volume 6, Issue 2 (2016)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 16071 "Pattern Avoidance and Genome Sorting".
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Michael Albert, Miklós Bóna, István Miklós, and Einar Steingrimsson. Pattern Avoidance and Genome Sorting (Dagstuhl Seminar 16071). In Dagstuhl Reports, Volume 6, Issue 2, pp. 65-77, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Article{albert_et_al:DagRep.6.2.65,
  author =	{Albert, Michael and B\'{o}na, Mikl\'{o}s and Mikl\'{o}s, Istv\'{a}n and Steingrimsson, Einar},
  title =	{{Pattern Avoidance and Genome Sorting (Dagstuhl Seminar 16071)}},
  pages =	{65--77},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2016},
  volume =	{6},
  number =	{2},
  editor =	{Albert, Michael and B\'{o}na, Mikl\'{o}s and Mikl\'{o}s, Istv\'{a}n and Steingrimsson, Einar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.6.2.65},
  URN =		{urn:nbn:de:0030-drops-58615},
  doi =		{10.4230/DagRep.6.2.65},
  annote =	{Keywords: evolutionary distance, lists, metrics, patterns, permutations, sorting}
}
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