相关论文: Separator-based derivations of graphic arrangement…

In this note we study the logarithmic derivation module of a non-free arrangement. We prove a generalized addition theorem for all arrangements. This addition theorem allows us to find various relationships between non-free arrangements,…

A graphic arrangement is a subarrangement of the braid arrangement whose set of hyperplanes is determined by an undirected graph. A classical result due to Stanley, Edelman and Reiner states that a graphic arrangement is free if and only if…

This paper studies the algebraic structure of a new class of hyperplane arrangement $A$ obtained by deleting two hyperplanes from a free arrangement. We provide information on the minimal free resolutions of the logarithmic derivation…

In this article, we study freeness of hyperplane arrangements. One of the most investigated arrangement is a graphic arrangement. Stanley proved that a graphic arrangement is free if and only if the corresponding graph is chordal and Dirac…

In these notes we study hyperplane arrangements having at least one logarithmic derivation of degree two that is not a combination of degree one logarithmic derivations. It is well-known that if a hyperplane arrangement has a linear…

We investigate arrangements of hyperplanes whose normal vectors are given by connected subgraphs of a fixed graph. These include the resonance arrangement and certain ideal subarrangements of Weyl arrangements. We characterize those which…

Athanasiadis studied arrangements obtained by adding shifted hyperplanes to the braid arrangement. Similarly, Bailey studied arrangements obtained by adding tilted hyperplanes to the braid arrangement. These two kinds of arrangements are…

Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and…

We define a chain complex for generalized splines on graphs, analogous to that introduced by Billera and refined by Schenck-Stillman for splines on polyhedral complexes. The hyperhomology of this chain complex yields bounds on the…

Discriminantal arrangements are hyperplane arrangements, which are generalized braid ones. They are constructed from given hyperplane arrangements, but their combinatorics are not invariant under combinatorial equivalence. However, it is…

This paper studies \emph{Dirichlet arrangements}, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We generalize descriptions of combinatorial features of graphic…

We introduce a new class of arrangements of hyperplanes, called (strictly) plus-one generated arrangements, from algebraic point of view. Plus-one generatedness is close to freeness, i.e., plus-one generated arrangements have their…

In his paper and thesis in 1989, Ziegler posed several conjectures regarding commutative algebra related to hyperplane arrangements. In this article, we revisit two of them. One is on generic cuts of free arrangements, and the other has to…

We define specific multiplicities on the braid arrangement by using edge-bicolored graphs. To consider their freeness, we introduce the notion of bicolor-eliminable graphs as a generalization of Stanley's classification theory of free…

Derivatives of computer graphics, image processing, and deep learning algorithms have tremendous use in guiding parameter space searches, or solving inverse problems. As the algorithms become more sophisticated, we no longer only need to…

Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…

The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum of given functions evaluated at the subgraph degrees. Here we study this problem by replacing degree sequences, via suitable nonlinear…

Separation logics are widely used for verifying programs that manipulate complex heap-based data structures. These logics build on so-called separation algebras, which allow expressing properties of heap regions such that modifications to a…

We prove using an extension of Saito's criterion that the algebra of differential operators tangent to a free hyperplane arrangement is generated by the derivations of the arrangement, recovering in this way a result of F. J.…

We present new degree-sequence lower bounds on the expected size of an independent set from the hard-core model. For arbitrary graphs, we establish a multivariate lower bound inspired by a conjecture of the first author and Kang and a…