Last edited by Kigakazahn
Monday, July 13, 2020 | History

4 edition of Transversals of infinite families with finitely many infinite members found in the catalog.

Transversals of infinite families with finitely many infinite members

Jon H. Folkman

# Transversals of infinite families with finitely many infinite members

## by Jon H. Folkman

Written in English

Subjects:
• Combinatorial analysis,
• Set theory

• Edition Notes

Bibliography: p. 32.

Classifications The Physical Object Statement [by] Jon Folkman. LC Classifications Q180.A1 R36 no. 5676, QA164 R36 no. 5676 Pagination vii, 32 p. Number of Pages 32 Open Library OL3890245M LC Control Number 81451626

The common opinion (I believe) is that such groups do exist, but the best result in this direction so far is the Olshanskii-Sapir group, which is finitely presented and (infinite torsion)-by-cyclic. There is a general idea, commonly attributed to Rips, which shows that such groups should exist. Finitely presented infinite simple groups.. [G Higman] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Book: All Authors / Contributors: G Higman. Find more information about: ISBN: OCLC .

Folkman, Transversals of infinite families with fmitely many infinite members, J. Combinatorial Theory 9 (), [3] M. Hall, Distinct representatives of subsets, Bull.   The problem of representing an integer as a sum of squares of integers is one of the oldest and most significant in mathematics. It goes back at least years to Diophantus, and continues more recently with the works of Fermat, Euler, Lagrange, Jacobi, Glaisher, Ramanujan, Hardy, Mordell, Andrews, and others. Jacobi's elliptic function approach dates from his epic Fundamenta Nova of

Cantor also proved that sets cannot be members of themselves and that there are sets which have more members that the denumerably infinite set of all the real numbers. In other words, that infinite sets are organized in a hierarchy. Russel and Whitehead concluded that mathematics was a branch of the logic of sets and that it is analytical. Infinity is paradoxical in many ways. Some paradoxes involve deterministic supertasks, such as Thomson's Lamp, where a switch is toggled an infinite number of times over a finite period of time, or the Grim Reaper, where it seems that infinitely many reapers can produce a result without doing anything. Others involve infinite lotteries. If you get two tickets from an infinite fair lottery.

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### Transversals of infinite families with finitely many infinite members by Jon H. Folkman Download PDF EPUB FB2

Abstract In this note we show by a simple direct proof that Folkman's necessary and sufficient condition for an infinite family of sets with finitely many infinite members to have a transversal implies Woodall's condition.

A short proof of. for a family with only finitely many infinite members to have a transversal. Our main result is THEOREM 1.

Let A = {Ai}i~i be a family of subsets of a set E. Suppose there is a set Io C I such that I -- Io is finite and Ai is finite for each i e Io. It is also shown that the existence of a transversal of an infinite family of sets with only countably many infinite members is equivalent to the existence of a function from the subsets of the index set of one family to the cardinal numbers having certain properties.

Note on a theorem of J. Folkman on transversals of infinite families with finitely many infinite members Article (PDF Available) in Journal of Combinatorial Theory Series B 30(1) February Author: François Bry. Bry, François (Februar ): Note on a theorem of J.

Folkman on transversals of infinite families with finitely many infinite members. In: Journal of Combinatorial Theory - Series B, Vol. 30, Nr. 1:. sufficient condition for an infinite family of sets with finitely many infinite members to have a transversal implies Woodall’s condition.

A short proof of Folkman’s theorem results by combining with Woodall’s proof. Several authors, Brualdi and Scrimger [ 11, Folkman [2] and Woodall [5]. partial transversals of two families 31 and 33 of subsets of a set E are investigated.

an infinite set but At is a finite set (i e I), the solution is a special case of Mirsky's that is members of ê which are maximal with respect to set-theoretic inclusion. Take your infinite set to be the nodes of an infinite binary tree, and take your sets to be the paths from the root to infinity.

Every two such paths will go separate ways after finitely many steps. Take your infinite set to be the quarter-lattice $\mathbf{N}^2$, and take your sets, indexed by $\theta\in[0,\pi/2)$, to consist of the lattice.

Is it obvious that a finitely generated group has only finitely many torsion elements. EDIT: Thanks to Jim Belk's answer, I know that being finitely generated isn't enough to have finitely many torsion elements for groups.

The next obvious question is "do there exist finitely-generated, infinite torsion groups of bounded exponent?". This. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share. We also show that the existence of a transversal of an infinite family of sets with only countably many infinite members is equivalent to the existence of a function from the subsets of the index set of the family to the cardinal numbers having certain the introduction we state the most important known results in this area.

JOURNAL OF COMBINATORIAL THEORY (B) 15, () Transversals of Infinite Families P. MCCARTHY* University of Kansas, Lawrence, Kansas Communicated by W. Tutte Received August 8, Let 21 be a family. The main theorem of this memorandum gives necessary and sufficient conditions for an infinite family of sets with only finitely many infinite members to have a transversal.

Folkman, K.J. () Transversals of Infinite Families With Finitely Many Infinite Members. RAND Corp. memorandum, RM — — PR Google Scholar 8. Gale, D., Shapley, L. () College Admissions and the Stability of Marriage.

So given an infinite number of countable sets X1, X2, X3, order the elements of Xi as xi1, xi2, xi3, and so on We can write any element of the set of the union of these sets as (x1k1, x2k2, x3k3, ), allowing an Xi to be "missed" if it does not feature in the element.

Insofar as this book (a very brief book indeed, with pages) is about games, we as a readers are players also, so maybe there are as many readings as readers. Or almost. Yet, it remains (or let) something that to me is unequivocal: life can be seen as a game so it has rules.

This book propose that rules in a temporal basis (finite vs. infinite).Reviews: Several authors, Brualdi and Scrimger [ 11, Folkman and Woodall, have given necessary and sufficient conditions for an infinite family of sets with finitely many infinite members to have a transversal, generalising the well-known theorems of Hall [ 3] and Jung and Rado [4 1.

In each case the proof of necessity is straightforward. Infinite families of biembedding numbers Infinite families of biembedding numbers Anderson, I. Let N(γ, γ′) denote the size of the smallest complete graph that cannot be edge‐partitioned into two parts embeddable in closed orientable sufaces of genera γ, γ′, respectively.

Well‐known embedding theorems are used to obtain several infinite families of values of N. Cardinality of Infinite Sets. The cardinality of a set is n (A) = x, where x is the number of elements of a set A. The cardinality of an infinite set is n (A) = ∞ as the number of elements is unlimited in it.

Properties of Infinite Sets. The union of two infinite sets is infinite; The power set of an infinite set is infinite. SIMPLE GROUPS OF INFINITE SQUARE WIDTH 5 following properties of z 1,z 2 (some necessary, other just convenient) shall benoted: (1) [z1],[z 2.

For infinite families of infinite sets very little is known. For what there is, see [1], [4], and [12]. s a well-known corollary to Theorem 1 giving some regularity conditions which are sufficient for a transversal to exist. (Si)iE, be a family of subsets of a set E = {e;};Ej.

J. Folkman, Transversals of infinite families with only finitely many infinite members, J. Comb. Theory, 9 (), – MathSciNet CrossRef zbMATH Google Scholar [7].Transversals of Infinite Families with Finitely Many Infinite Members. Graphs with Monochromatic Complete Subgraphs in Every Edge Coloring.

Edge colorings in bipartite graphs Regular Line Symmetric Graphs. A limit theorem for subadditive collections of .