Related papers: Centrally Image partition Regularity near 0
We prove a central limit theorem for smooth linear statistics associated with zero divisors of standard Gaussian holomorphic sections in a sequence of holomorphic line bundles with Hermitian metrics of class $\mathscr{C}^{3}$ over a compact…
A normal partition of the edges of a cubic graph is a partition into trails (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition. We investigate this notion and give some results and problems.
We study a bijective map from integer partitions to the prime factorizations of integers that we call the "supernorm" of a partition, in which the multiplicities of the parts of partitions are mapped to the multiplicities of prime factors…
Image restoration problems are typically ill-posed requiring the design of suitable priors. These priors are typically hand-designed and are fully instantiated throughout the process. In this paper, we introduce a novel framework for…
Furstenberg introduced the notion of Central sets in 1981. Later in 1990 V. Bergelson and N. Hindman proved a different but an equivalent version of the central set theorem. In 2008 D. De, N. Hindman and D. Strauss proved a stronger version…
The study of the size of subsets in a semigroup have shown that many of these subsets have strong combinatorial properties and contribute richly to the algebraic structure of the Stone-Cech compactification of a discrete semigroup. N.…
The problem of image segmentation is known to become particularly challenging in the case of partial occlusion of the object(s) of interest, background clutter, and the presence of strong noise. To overcome this problem, the present paper…
The Satisfactory Partition problem consists in deciding if the set of vertices of a given undirected graph can be partitioned into two nonempty parts such that each vertex has at least as many neighbours in its part as in the other part.…
The notion of central stability was first formulated for sequences of representations of the symmetric groups by Putman. A categorical reformulation was subsequently given by Church, Ellenberg, Farb, and Nagpal using the notion of…
Hindman and Leader first introduced the notion of semigroup of ultrafilters converging to zero for a dense subsemigroups of $((0,\infty),+)$. Using the algebraic structure of the Stone-$\breve{C}$ech compactification, Tootkabani and Vahed…
An internal or friendly partition of a graph is a partition of the vertex set into two nonempty sets so that every vertex has at least as many neighbours in its own class as in the other one. It has been shown that apart from finitely many…
Combinatorially Rich sets were introduced by Bergelson and Glasscock for commutative semigroup. Latter Hindman, Hosseini, Strauss and Tootkaboni extended the definition of Combinatorially Rich sets for arbitrary semigroup. Recently Goswami…
In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…
Image segmentation refers to the process to divide an image into nonoverlapping meaningful regions according to human perception, which has become a classic topic since the early ages of computer vision. A lot of research has been conducted…
An integer partition of $n$ is called graphical if its parts form a degree sequence of a simple graph. While unrestricted graphical partitions have been extensively studied, much less is known when the parts are restricted to a prescribed…
There exist two notions of typicality in computability theory, namely, genericity and randomness. In this article, we introduce a new notion of genericity, called partition genericity, which is at the intersection of these two notions of…
Optimal matrices for problems involving the matrix numerical radius often have fields of values that are disks, a phenomenon associated with partial smoothness. Such matrices are highly structured: we experiment in particular with the…
A perfect $H$-tiling in a graph $G$ is a collection of vertex-disjoint copies of a graph $H$ in $G$ that together cover all the vertices in $G$. In this paper we investigate perfect $H$-tilings in a random graph model introduced by Bohman,…
The non-centralizer graph of a finite group $G$ is the simple graph $\Upsilon_G$ whose vertices are the elements of $G$ with two vertices $x$ and $y$ are adjacent if their centralizers are distinct. The induced subgroup of $\Upsilon_G$…
Using the methods from topological dynamics, H. Furstenberg introduced the notions of Central sets and proved the famous Central Sets Theorem which is the simultaneous extension of the van der Waerden and Hindman Theorem. Later N. Hindman…