Asymptotics of symmetry in matroids

Pendavingh, RA Rudi; Pol, JG Jorn van der

doi:10.1016/j.jctb.2018.09.001

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Asymptotics Of Matroid Automorphism Groups1

Introduction1

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2021

2023

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Cited by 3 publications

(2 citation statements)

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“…It is conjectured in [10] that asymptotically almost all matroids have a trivial automorphism group, and some progress on this is made in [12]; in particular, they show that asymptotically almost all sparse-paving matroids have trivial automorphism group (and it is conjectured in [10] that almost all matroids are sparse-paving).…”

Section: Asymptotics Of Matroid Automorphism Groupsmentioning

confidence: 99%

The virtual Euler characteristic for binary matroids

Brandt¹,

Bruce²,

Corey³

2023

Preprint

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Inspired by Kontsevich's graphic orbifold Euler characteristic we define a virtual Euler characteristic for any finite set of isomorphism classes of matroids of rank r. Our main result provides a simple formula for the virtual Euler characteristic for the set of isomorphism classes of matroids of rank r realizable over F 2 (i.e., binary matroids). We prove this formula by relating the virtual Euler characteristic for binary matroids to the point counts of certain subsets of Grassmanians over finite fields. We conclude by providing several follow-up questions in relation to matroids realizable over other finite prime fields, matroid homology, and beta invariants.

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Section: Asymptotics Of Matroid Automorphism Groupsmentioning

confidence: 99%

The virtual Euler characteristic for binary matroids

Brandt¹,

Bruce²,

Corey³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…This count is derived from the computation of other important combinatorial invariants: Betti numbers and characteristic polynomials [1,19,28,36,42,44]. While most arrangements admit few combinatorial symmetries [38], most arrangements of interest do [17,39,45].…”

Section: Introductionmentioning

confidence: 99%