相关论文: Irreducibility of configurations
Cubic bipartite graphs with girth at least 6 correspond to symmetric combinatorial (v_3) configurations. In 1887 V. Martinetti described a simple reduction method which enables one to reduce each combinatorial (v_3) configuration to one…
We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…
A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
Reversible computing is motivated by both pragmatic and foundational considerations arising from a variety of disciplines. We take a particular path through the development of reversible computation, emphasizing compositional reversible…
For readers already familiar with Partial Information Decomposition (PID), we show that PID's definition of synergy enables quantifying at least four different notions of irreducibility. First, we show four common notions of "parts" give…
Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in…
This is the fourth in a series of papers math.AG/0312190, math.AG/0503029, math.AG/0410267 on configurations in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration is a finite collection of objects and…
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the…
In 1985 Joe Harris proved the long standing claim of Severi that equisingular families of nodal plane curves are irreducible whenever they are non-empty. For families with more complicated singularities this is no longer true. Given a…
Graph manifolds are a class of compact, orientable 3-manifolds introduced in 1967 by Waldhausen as a generalization of Seifert fibered 3-manifolds. From the point of view of Thurston's geometrization program, graph manifolds are exactly the…
A relational structure ${\mathbb X}$ is said to be reversible iff every bijective endomorphism $f:X\rightarrow X$ is an automorphism. We define a sequence of non-zero cardinals $\langle \kappa_i :i\in I\rangle$ to be reversible iff each…
We show how ideas coming out of gauge theory can be used to prove configurations in the list of ``633 unavoidable configurations" are reducible. In this paper, we prove the smallest nontrivial example, the Birkhoff diamond, is reducible…
Irreducible representations are the building blocks of general, semisimple Galois representations \rho, and cuspidal representations are the building blocks of automorphic forms \pi of the general linear group. It is expected that when an…
Martingale transport plans on the line are known from Beiglbock & Juillet to have an irreducible decomposition on a (at most) countable union of intervals. We provide an extension of this decomposition for martingale transport plans in R^d,…
The stability number of a forbidden family measures how many different structures are needed to approximate all near-extremal constructions avoiding it. An infinite stability number means that no finite list of structures suffices. We…
We present a new construction of triple arrays by combining a symmetric 2-design with a resolution of another 2-design. This is the first general method capable of producing non-extremal triple arrays. We call the triple arrays which can be…
Answering some of the main questions from [MR13], we show that whenever $\kappa$ is a cardinal satisfying $\kappa^{< \kappa} = \kappa > \omega$, then the embeddability relation between $\kappa$-sized structures is strongly invariantly…
We give necessary and sufficient topological conditions for the existence of an irreducible ${\rm SO}(3)$-structure on a $5$-manifold. Using these conditions we provide some new examples of $5$-manifolds with an irreducible ${\rm…
A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is…
This is the first paper that provides a systematic treatment of the $r$-dimensional PTE problem in additive number theory, abbreviated by PTE$_r$, through its connection with combinatorial design theory, the branch of combinatorial…