Results 41 to 50 of about 9,755 (179)
A tropical approach to rigidity: Counting realisations of frameworks
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A realisation of a graph in the plane as a bar‐joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely many realisations can be seen as a solution to a system of quadratic equations prescribing the distances between pairs of points.
Oliver Clarke +6 more
wiley +1 more source
Detection of Emergent Situations in Complex Systems by Structural Invariant (MB, M)
Mendel, 2017 The paper introduces complete description of the detection method that uses structural invariant Matroid and its Bases (MB, M). There are recapitulated essential concepts from the used knowledge field as “complex system, emergent situations (A, B, C ...
Jiri Bila, Martin Novak
doaj +1 more source
Weakly Submodular Functions [PDF]
, 2014 Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions, which we call {\em
Borodin, Allan +2 more
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Toric amplitudes and universal adjoints
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A toric amplitude is a rational function associated with a simplicial polyhedral fan. The definition is inspired by scattering amplitudes in particle physics. We prove algebraic properties of such amplitudes and study the geometry of their zero loci. These hypersurfaces play the role of Warren's adjoint via a dual volume interpretation.
Simon Telen
wiley +1 more source
On higher Jacobians, Laplace equations, and Lefschetz properties
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Let A$A$ be a standard graded Artinian K$\mathbb {K}$‐algebra over a field of characteristic zero. We prove that the failure of strong Lefschetz property (SLP) for A$A$ is equivalent to the osculating defect of a certain rational variety.
Charles Almeida +2 more
wiley +1 more source
Connectedness of graphs and its application to connected matroids through covering-based rough sets [PDF]
, 2015 Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree.
Huang, Aiping, Zhu, William
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Gromov–Witten theory and invariants of matroids
Selecta Mathematica, 2022 AbstractWe use techniques from Gromov–Witten theory to construct new invariants of matroids taking value in the Chow groups of spaces of rational curves in the permutohedral toric variety. When the matroid is realizable by a complex hyperplane arrangement, our invariants coincide with virtual fundamental classes used to define the logarithmic Gromov ...
Ranganathan, Dhruv, Usatine, Jeremy
openaire +4 more sources
Canonical forms of oriented matroids
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Positive geometries are semialgebraic sets equipped with a canonical differential form whose residues mirror the boundary structure of the geometry. Every full‐dimensional projective polytope is a positive geometry. Motivated by the canonical forms of polytopes, we construct a canonical form for any tope of an oriented matroid inside the Orlik–
Christopher Eur, Thomas Lam
wiley +1 more source
Matroidal structure of generalized rough sets based on symmetric and transitive relations [PDF]
, 2012 Rough sets are efficient for data pre-process in data mining. Lower and upper approximations are two core concepts of rough sets. This paper studies generalized rough sets based on symmetric and transitive relations from the operator-oriented view by ...
Yang, Bin, Zhu, William
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