相关论文: The Free product of Matroids

We establish a duality between monads and monadic morphisms in any $(\infty,2)$-category and characterize monadic morphisms in a wide class of examples. This duality unifies several dualities between algebraic structures and their…

Binary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid…

Komj\'ath, Milner, and Polat investigated when a finitary matroid admits a partition into circuits. They defined the class of ``finite matching extendable'' matroids and showed in their compactness theorem that those matroids always admit…

The class of free multiarrangements is known to be closed under taking localizations. We extend this result to the stronger notions of inductive and recursive freeness. As an application, we prove that recursively free multiarrangements are…

Generalizing a theorem of Macdonald, we show a formula for the mixed Hodge structure on the cohomology of the symmetric products of bounded complexes of mixed Hodge modules by showing the existence of the canonical action of the symmetric…

The von Neumann algebra free product of arbitary finite dimensional von Neumann algebras with respect to arbitrary faithful states, at least one of which is not a trace, is found to be a type~III factor possibly direct sum a finite…

We prove that if $ M $ and $ N $ are finitary matroids on a common countable edge set $ E $ then they admit a common independent set $I $ such that there is a bipartition $ E=E_{M}\cup E_{N} $ for which $ I\cap E_M $ spans $ E_M $ in $ M $…

Residual torsion-free nilpotence has proven to be an important property for knot groups with applications to bi-orderability and ribbon concordance. Mayland proposed a strategy to show that a two-bridge knot group has a commutator subgroup…

In this paper, we consider some non-weight modules over the Lie algebra of Weyl type. First, we determine the modules whose restriction to $U(\frak h)$ are free of rank $1$ over the Lie algebra of differential operators on the circle. Then…

Is it possible to define cryptomorphic axiom systems for infinite oriented matroids by lifting some of the axiom systems for finite oriented matroids to the infinite setting while not losing duality in the process? We show that the answer…

We introduce real second-order freeness in second-order noncommutative probability spaces. We demonstrate that under this definition, three real models of random matrices, namely real Ginibre matrices, Gaussian orthogonal matrices, and real…

Matroids and semigraphoids are discrete structures abstracting and generalizing linear independence among vectors and conditional independence among random variables, respectively. Despite the different nature of conditional independence…

An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair. For pairs for which neither matroid can be obtained, up to isomorphism, from the other…

A fundamental theorem of matroid theory establishes that a transversal matroid is representable over fields of any characteristic. It was proved in 1970 by Piff and Welsh: their proof is elegant and concise and, moveover, constructive.…

The matroid-based valuation conjecture of Ostrovsky and Paes Leme states that all gross substitutes valuations on $n$ items can be produced from merging and endowments of weighted ranks of matroids defined on at most $m(n)$ items. We show…

In 2004, Ehrenfeucht, Harju, and Rozenberg showed that any graph on a vertex set $V$ can be obtained from a complete graph on $V$ via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local…

We consider general bilinear products defined by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and include the classical Hadamard, Kronecker, and convolutional…

We introduce the matroid-minor coalgebra C, which has labeled matroids as distinguished basis, and coproduct given by splitting a matroid into a submatroid and complementary contraction all possible ways. We introduce two new bases for C;…

This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a…

We show that various combinatorial invariants of matroids such as Chow rings and Orlik--Solomon algebras may be assembled into "operad-like" structures. Specifically, one obtains several operads over a certain Feynman category which we…