Results 41 to 50 of about 275 (182)
Advances in Applied MathematicsWe show that an adjoint of a loopless matroid is connected if and only if it itself is connected. Our first goal is to study the adjoint of modular matroids. We prove that a modular matroid has only one adjoint (up to isomorphism) which can be given by its opposite lattice, and proceed to present some alternative characterizations of modular matroids ...
Houshan Fu, Chunming Tang, Suijie Wang
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Fine multidegrees, universal Gröbner bases, and matrix Schubert varieties
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract We give a criterion for a collection of polynomials to be a universal Gröbner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in (P1)N$(\mathbb {P}^1)^N$. This criterion can be used to give simple proofs of several existing results on universal Gröbner bases.
Daoji Huang, Matt Larson
wiley +1 more source
Orthogonal matroids over tracts
Forum of Mathematics, SigmaWe generalize Baker–Bowler’s theory of matroids over tracts to orthogonal matroids, define orthogonal matroids with coefficients in tracts in terms of Wick functions, orthogonal signatures, circuit sets and orthogonal vector sets, and establish basic ...
Tong Jin, Donggyu Kim
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The Chip Firing Game and Matroid Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper we construct from a cographic matroid M, a pure multicomplex whose degree sequence is the h―vector of the the matroid complex of M. This result provesa conjecture of Richard Stanley [Sta96] in the particular case of cographic matroids.
Criel Merino
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Linear Algebraic Relations among Cardinalities of Sets of Matroid Functions
Mathematics, 2023 We introduce a unifying approach for invariants of finite matroids that count mappings to a finite set. The aim of this paper is to show that if the cardinalities of mappings with fixed values on a restricted set satisfy contraction–deletion rules, then ...
Martin Kochol
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How to see the forest despite the trees
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract One of the major starting points of discrete optimization is the theorem of Nash‐Williams and Tutte on the existence of k$k$ disjoint spanning trees of a graph, along with its counterpart on the existence of k$k$ forests covering all edges of the graph.
Erika Bérczi‐Kovács, András Frank
wiley +1 more source
Base Axioms of Modular Supermatroids
Journal of Applied Mathematics, 2014 This paper studies axiom systems of supermatroids. Barnabei et al.'s base axioms concerning poset matroids (i.e., distributive supermatroids) are generalized to modular supermatroids, and a mistake in the proof of base axioms of poset matroids is pointed
Xiaonan Li, Sanyang Liu
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Interval positroid varieties and a deformation of the ring of symmetric functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Define the interval rank $r_[i,j] : Gr_k(\mathbb C^n) →\mathbb{N}$ of a k-plane V as the dimension of the orthogonal projection $π _[i,j](V)$ of V to the $(j-i+1)$-dimensional subspace that uses the coordinates $i,i+1,\ldots,j$.
Allen Knutson, Mathias Lederer
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Lower bounds for cube‐ideal set‐systems
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract A set‐system S⊆{0,1}n$S\subseteq \lbrace 0,1\rbrace ^n$ is cube‐ideal if its convex hull can be described by capacity and generalized set covering inequalities. In this paper, we use combinatorics, convex geometry, and polyhedral theory to give exponential lower bounds on the size of cube‐ideal set‐systems, and linear lower bounds on their ...
Ahmad Abdi +3 more
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Duality, Matroids, Qubits, Twistors, and Surreal Numbers
Frontiers in Physics, 2018 We show that via the Grassmann-Plücker relations, the various apparent unrelated concepts, such as duality, matroids, qubits, twistors, and surreal numbers are, in fact, deeply connected. Moreover, we conjecture the possibility that these concepts may be
J. A. Nieto
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