Logarithmic concavity for morphisms of matroids

Eur, Christopher; Huh, June

doi:10.1016/j.aim.2020.107094

Cited by 17 publications

(14 citation statements)

References 19 publications

(13 reference statements)

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“…We remark that, unlike[BGW03] but in agreement with[EH20] and[CDMS20], we allow repetition of matroids in the sequence of matroids that constitute a flag matroid.…”

mentioning

confidence: 84%

“…In this paper, by morphisms of matroids we will mean matroid quotients, as defined below 1 . They generalize the graph homomorphisms, linear maps, and graphs embedded on surfaces; see [EH20] for illustrations of these examples. Definition 2.1.…”

Section: Preliminaries: Flag Matroids and Their K-classes On Flag Var...mentioning

confidence: 99%

“…For a more on matroid quotients, we refer the reader to [Bry86,§7.4] or [Oxl11,§7.3]. 1 The behavior of a morphism of matroids, in a more general sense of [EH20] or [HP18], is largely governed by an associated matroid quotient [EH20, Lemma 2.4].…”

Section: Preliminaries: Flag Matroids and Their K-classes On Flag Var...mentioning

confidence: 99%

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K-theoretic Tutte polynomials of morphisms of matroids

Dinu¹,

Eur²,

Seynnaeve³

2020

Preprint

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We generalize the Tutte polynomial of a matroid to a morphism of matroids via the K-theory of flag varieties. We show that there are two different generalizations, and demonstrate that each has its own merits, where the trade-off is between the ease of combinatorics and geometry. One generalization recovers the Las Vergnas Tutte polynomial of a morphism of matroids, which admits a corank-nullity formula and a deletion-contraction recursion. The other generalization does not, but better reflects the geometry of flag varieties.Faculty of Mathematics and Computer Science,

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“…We remark that, unlike[BGW03] but in agreement with[EH20] and[CDMS20], we allow repetition of matroids in the sequence of matroids that constitute a flag matroid.…”

mentioning

confidence: 84%

Section: Preliminaries: Flag Matroids and Their K-classes On Flag Var...mentioning

confidence: 99%

See 1 more Smart Citation

K-theoretic Tutte polynomials of morphisms of matroids

Dinu¹,

Eur²,

Seynnaeve³

2020

Preprint

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“…In [1], Lorentzian polynomials were used to give a generalization of Postnikov's formula for the volume of a generalized permutahedron, a beautiful polytope studied extensively in [9]. In [4], Lorentzian polynomials were also used to prove a generalization of Mason's conjecture on the f -vectors of independent subsets of matroids.…”

Section: Introductionmentioning

confidence: 99%

Lorentzian polynomials from polytope projections

Mészáros¹,

Setiabrata²

2021

Algebraic Combinatorics

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Lorentzian polynomials, recently introduced by Brändén and Huh, generalize the notion of log-concavity of sequences to homogeneous polynomials whose supports are integer points of generalized permutahedra. Brändén and Huh show that normalizations of integer point transforms of generalized permutahedra are Lorentzian. Moreover, normalizations of certain projections of integer point transforms of generalized permutahedra with zero-one vertices are also Lorentzian. Taking this polytopal perspective further, we show that normalizations of certain projections of integer point transforms of flow polytopes are Lorentzian.

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“…Recent years have seen growing interest in categorical aspects of matroids (e.g. see [HP18;EH20]). In a previous paper, the authors (with M. Szczesny) studied the category of finite matroids with strong maps in connection with combinatorial Hopf algebras, and initiated the study of algebraic K-theory for finite matroids.…”

Section: Introductionmentioning

confidence: 99%

On Infinite Matroids with Strong Maps: Proto-exactness and Finiteness Conditions

Eppolito,

Jun

2021

Preprint

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This paper investigates infinite matroids from a categorical perspective. We prove that the category of infinite matroids is a proto-exact category in the sense of Dyckerhoff and Kapranov, thereby generalizing our previous result on the category of finite matroids. We also characterize finitary matroids as co-limits of finite matroids, and show that the finite matroids are precisely the finitely presentable objects in this category.

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Logarithmic concavity for morphisms of matroids

Cited by 17 publications

References 19 publications

K-theoretic Tutte polynomials of morphisms of matroids

K-theoretic Tutte polynomials of morphisms of matroids

Lorentzian polynomials from polytope projections

On Infinite Matroids with Strong Maps: Proto-exactness and Finiteness Conditions

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