Asymptotics of symmetry in matroids

Rudi Pendavingh; Jorn van der Pol

doi:10.1016/j.jctb.2018.09.001

Asymptotics of symmetry in matroids

Rudi Pendavingh (Corresponding author), Jorn van der Pol (Corresponding author)

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Abstract

We prove that asymptotically almost all matroids have a trivial automorphism group, or an automorphism group generated by a single transposition. Additionally, we show that asymptotically almost all sparse paving matroids have a trivial automorphism group.

Original language	English
Pages (from-to)	349-365
Number of pages	17
Journal	Journal of Combinatorial Theory, Series B
Volume	135
DOIs	https://doi.org/10.1016/j.jctb.2018.09.001
Publication status	Published - 1 Mar 2019

Keywords

Asymptotic enumeration
Automorphism group
Matroid
Symmetry

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10.1016/j.jctb.2018.09.001

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title = "Asymptotics of symmetry in matroids",

abstract = "We prove that asymptotically almost all matroids have a trivial automorphism group, or an automorphism group generated by a single transposition. Additionally, we show that asymptotically almost all sparse paving matroids have a trivial automorphism group.",

keywords = "Asymptotic enumeration, Automorphism group, Matroid, Symmetry",

author = "Rudi Pendavingh and \{van der Pol\}, Jorn",

year = "2019",

month = mar,

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doi = "10.1016/j.jctb.2018.09.001",

language = "English",

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journal = "Journal of Combinatorial Theory, Series B",

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T1 - Asymptotics of symmetry in matroids

AU - Pendavingh, Rudi

AU - van der Pol, Jorn

PY - 2019/3/1

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AB - We prove that asymptotically almost all matroids have a trivial automorphism group, or an automorphism group generated by a single transposition. Additionally, we show that asymptotically almost all sparse paving matroids have a trivial automorphism group.

KW - Asymptotic enumeration

KW - Automorphism group

KW - Matroid

KW - Symmetry

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U2 - 10.1016/j.jctb.2018.09.001

DO - 10.1016/j.jctb.2018.09.001

M3 - Article

AN - SCOPUS:85053331583

SN - 0095-8956

VL - 135

SP - 349

EP - 365

JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

ER -

Asymptotics of symmetry in matroids

Abstract

Keywords

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