1,727,041 research outputs found
Erdos-Ko-Rado from intersecting shadows
No full textA set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdos-Ko-Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corresponding results
Computational advances in Rado numbers
No full textIn this dissertation, we present new methods in the computation of Rado numbers. These methods are applied to several families of equations. The Rado number of an equation is a Ramsey-theoretic quantity associated to the equation. For any particular equation E, the Rado number R_r(E) is the smallest N such that any r-coloring chi:{1,2,...,N} -> {1,2,...,r} must induce a monochromatic solution to E. We will lay out the history of this field and provide some structure as context for new results. Then we will discuss the new methods and computational tools that provide the foundation of the thesis. The 2-color Rado numbers R_2(2x+2y+kz = 3w) and R_2(kx+(k+1)y = (k+2)z) are computed for small values of the parameter k. The 2-color off-diagonal Rado numbers R_2(x + ay = z; x + by = z) are provided for 1 = (3^r - 1)(c+1)/2 for c >= 0. We also compute the precise values for r = 4 and -20 = 3 variables. We provide the 2-color Rado numbers for 1/x + 1/y = 1/z and a few other equations involving reciprocals. We also construct a coloring proving R_2(x^2 + y^2 = z^2) > 6500. (It is not known whether this Rado number is finite.) We compute the 2- and 3-color Rado numbers for other sums-of-squares equations, sum_{i=1}^a x_i^2) = sum_{i=1}^b y_i^2, and we prove a universal upper bound for a <= b <= ca for a constant c between 1 and 2 (different values of c give different upper bounds). We follow this with Rado numbers for other assorted families of quadratic equations. We also present quantitative analogues of Hindman's theorem, which guarantees monochromatic solutions to systems like {x+y+z = w; x*y*z = v}. We conclude by suggesting a number of conjectures, extensions, and generalizations of these results for future work.Ph.D.Includes bibliographical referencesby Kellen John Myer
Elmo rado
No full textElmo Rado is a character who stars in a series of comics published on Instagram which seek to question male gender stereotypes through humor and irony. https://www.instagram.com/elmorad0/.Elmo Rado es un personaje que protagoniza una serie de cómics publicados en Instagram los cuales buscan cuestionar los estereotipos de género masculinos por medio del humor y la ironía. https://www.instagram.com/elmorad0/.Diseñador IndustrialPregrad
Erdős-Rado Classes
Get PDFWe amalgamate two generalizations of Ramsey\u27s Theorem--Ramsey classes and the Erdős-Rado Theorem--into the notion of a combinatorial Erdős-Rado class. These classes are closely related to Erdős-Rado classes, which are those from which we can build generalized indiscernibles and blueprints in nonelementary classes, especially Abstract Elementary Classes. We give several examples and some applications
Disjunctive Rado numbers
No full textAbstractIf L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1,L2} is the least integer n, provided that it exists, such that for every 2-coloring of the set {1,2,…,n} there exists a monochromatic solution to either L1 or L2. If such an integer n does not exist, then the disjunctive Rado number is infinite. In this paper, it is shown that for all integers a⩾1and b⩾1, the disjunctive Rado number for the equations x1+a=x2 and x1+b=x2 is a+b+1-gcd(a,b) if agcd(a,b)+bgcd(a,b) is odd and the disjunctive Rado number for these equations is infinite otherwise. It is also shown that for all integers a>1 and b>1, the disjunctive Rado number for the equations ax1=x2 and bx1=x2 is cs+t-1 if there exist natural numbers c,s, and t such that a=cs and b=ct and s+t is an odd integer and c is the largest such integer, and the disjunctive Rado number for these equations is infinite otherwise
An Overwiev Of The Rado Graph
No full textThis paper examines the Rado graph, the unique, countably infinite, universalgraph. Many of the central properties are covered in detail, and various constructionsare provided, using results from a variety of fields of mathematics. A variantof the Rado graph was initially constructed by Ackermann. The actual Rado graphwas studied later, by Erdős and Rényi, before Rado rediscovered it from a differentperspective. A multitude of other authors have since then contributed to the subject
Ex Libris, Antonii Rado von Ada Nigrin
No full textEX LIBRIS, ANTONII RADO VON ADA NIGRIN
Ex Libris, Antonii Rado von Ada Nigrin ( -
A Multidimensional Rado Theorem
Get PDFWe extend Deuber\u27s theorem on -sets to hold over the multidimensional positive integer lattices. This leads to a multidimensional Rado theorem where we are guaranteed monochromatic multidimensional points in all finite colorings of where the set of coordinates satisfies the given linear Rado system
On Erdős-Ko-Rado for random hypergraphs
No full textOn Erdős-Ko-Rado for Random Hypergraphs o by Arran Hamm Dissertation Director: Jeff Kahn Denote by Hk (n, p) the random k-graph in which each k-subset of {1, . . . , n} is present with probability p, independent of other choices. This dissertation addresses the question: for which p0 will Hk (n, p) satisfy the “Erd˝s-Ko-Rado property” provided that o p > p0 ? This question was first studied by Balogh, Bohman, and Mubayi where they dealt mainly with k 0). Our first main result gives the desired p0 when k 0 such that if n = 2k + 1 and p > 1 − ε, then Hk (n, p) has the EKR property a.s. iiPh.D.Includes bibliographical referencesby Arran Ham
Bilangan Rado untuk a(x+y)=bz
No full textBilangan Rado k−warna adalah bilangan asli terkecil n sedemikian sehingga terdapat solusi monokromatik pada 1,2,...,n. Bilangan Rado merupakan hasil perumuman dari bilangan Schur. Tulisan ini menyajikan beberapa bilangan Rado a(x + y) = bz untuk b = 2, b = a+1, juga membahas tentang barisan monokromatik Xn yang persamaannya diperumum menjadi persamaan linear rekursif orde 2 yaitu a(Xn + Xn+1) = bXn+2. Metode yang digunakan adalah analisis komputasi dasar yang menggunakan beberapa teori bilangan. Hasil penelitian merupakan bentuk umum dan nilai eksak untuk beberapa bilangan Rado a(x+y) = bz
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