Related papers: Counting point configurations in projective space
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
For complete affine manifolds we introduce a definition of compactification based on the projective differential geometry (i.e.\ geodesic path data) of the given connection. The definition of projective compactness involves a real parameter…
We study the enumeration of bargraphs with respect to some corner statistics. We find generating functions for the number of bargraphs that tracks the corner statistics of interest, the number of cells, and the number of columns. The…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs; in particular we draw heavily from the topic of dominating sets. Through…
Bipartite Graph is often a realistic model of complex networks where two different sets of entities are involved and relationship exist only two entities belonging to two different sets. Examples include the user-item relationship of a…
We compute stationary gravitational descendants in symplectic ellipsoids of any dimension, and use these to derive a number of new recursive formula for punctured curve counts in symplectic manifolds with ellipsoidal ends. Along the way we…
Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of…
From a group action on a space, define a variant of the configuration space by insisting that no two points inhabit the same orbit. When the action is almost free, this "orbit configuration space" is the complement of an arrangement of…
In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation…
Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we…
We consider bicolored maps, i.e. graphs which are drawn on surfaces, and construct a bijection between (i) oriented maps with arbitary face structure, and (ii) (weighted) non-oriented maps with exactly one face. Above, each non-oriented map…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
Welschinger invariants of the real projective plane can be computed via the enumeration of enriched graphs, called marked floor diagrams. By a purely combinatorial study of these objects, we prove a Caporaso-Harris type formula which allows…
We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary…
Point configurations have been widely used as model systems in condensed matter physics, materials science and biology. Statistical descriptors such as the $n$-body distribution function $g_n$ is usually employed to characterize the point…
Startpoints (resp. endpoints) can be defined as "oriented fixed points". They arise naturally in the study of fixed for multi-valued maps defined on quasi-metric spaces. In this article, we give a new result in the startpoint theory for…
We explore various techniques for counting the number of straight-edge crossing-free graphs that can be embedded on a planar point set. In particular, we derive a lower bound on the ratio of the number of such graphs with $m+1$ edges to the…
We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our…