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Broken Circuits in Matroids—Dohmen’s Inductive Proof
Discussiones Mathematicae Graph Theory, 2013 Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem.
Kordecki Wojciech +1 more
doaj +1 more source
Efficient and strategy‐proof mechanism under general constraints
Theoretical Economics, Volume 20, Issue 2, Page 481-509, May 2025.This study investigates efficient and strategy‐proof mechanisms for allocating indivisible goods under constraints. First, we examine a setting without endowments. In this setting, we introduce a class of constraints—ordered accessibility—for which the serial dictatorship (SD) mechanism is Pareto‐efficient (PE), individually rational (IR), and group ...
Kenzo Imamura, Yasushi Kawase
wiley +1 more source
On cographic matroids and signed-graphic matroids
Discrete Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
, 1992 Oriented matroids have been introduced in [R. G. Bland and M. Las Vergnas, Orientability of Matroids, J. Combin. Theory Ser. B24 (1978), 94–123]. They can be viewed as an abstraction of matroids representable over an ordered field. Analogously, we define
Wenzel, Walter +3 more
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New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker +2 more
wiley +1 more source
Templates for Binary Matroids [PDF]
, 2017 A binary frame template is a device for creating binary matroids from graphic or cographic matroids. Such matroids are said to conform or coconform to the template.
Van Zwam, Stefan H.M. +3 more
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Modifications of Tutte–Grothendieck invariants and Tutte polynomials
AKCE International Journal of Graphs and Combinatorics, 2020 Generalized Tutte–Grothendieck invariants are mappings from the class of matroids to a commutative ring that are characterized recursively by contraction–deletion rules. Well known examples are Tutte, chromatic, tension and flow polynomials.
Martin Kochol
doaj +1 more source
Matroids, positroids and paths [PDF]
, 2019 Matroids arise from the abstract notion of dependency. Matroids can be studied from different points of view. From linear algebra we know matrices, which can be seen as matroids, however matroids generalise the concept of dependency.
Ros Jiménez, Zaira
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On triangular matroids induced by n3-configurations
Open Mathematics, 2020 A triangular matroid is a rank-3 matroid whose ground set consists of the points of an n3{n}_{3}-configuration and whose bases are the point triples corresponding to non-triangles within the configuration.
Alazemi Abdullah, Raney Michael
doaj +1 more source
Quasi-Graphic Matroids (retracted)
, 2018 Frame matroids and lifted-graphic matroids are two interesting generalizations of graphic matroids. Here, we introduce a new generalization, quasi-graphic matroids, that unifies these two existing classes.
Geelen, Jim +5 more
core +1 more source