scholarly journals On the Number of Matroids Compared to the Number of Sparse Paving Matroids

10.37236/4899 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Rudi Pendavingh ◽  
Jorn Van der Pol
Keyword(s):  
Stable Set ◽  
Asymptotic Enumeration ◽  
Stable Sets ◽  
Johnson Graph ◽  
Johnson Graphs ◽  
Other Information ◽  
One To One ◽  
Almost All

It has been conjectured that sparse paving matroids will eventually predominate in any asymptotic enumeration of matroids, i.e. that $\lim_{n\rightarrow\infty} s_n/m_n = 1$, where $m_n$ denotes the number of matroids on $n$ elements, and $s_n$ the number of sparse paving matroids. In this paper, we show that $$\lim_{n\rightarrow \infty}\frac{\log s_n}{\log m_n}=1.$$ We prove this by arguing that each matroid on $n$ elements has a faithful description consisting of a stable set of a Johnson graph together with a (by comparison) vanishing amount of other information, and using that stable sets in these Johnson graphs correspond one-to-one to sparse paving matroids on $n$ elements.As a consequence of our result, we find that for all $\beta > \displaystyle{\sqrt{\frac{\ln 2}{2}}} = 0.5887\cdots$, asymptotically almost all matroids on $n$ elements have rank in the range $n/2 \pm \beta\sqrt{n}$.

scholarly journals Coalition formation and history dependence

2020 ◽  
Vol 15 (1) ◽  
pp. 159-197 ◽  
Author(s):  
Bhaskar Dutta ◽  
Hannu Vartiainen
Keyword(s):  
Coalition Formation ◽  
Stable Set ◽  
Transferable Utility ◽  
Stable Sets ◽  
Solution Concepts ◽  
History Dependence ◽  
Von Neumann ◽  
Finite Games ◽  
A Chain ◽  
Indirect Dominance

Farsighted formulations of coalitional formation, for instance, by Harsanyi and Ray and Vohra, have typically been based on the von Neumann–Morgenstern stable set. These farsighted stable sets use a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional “moves” in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra restricted coalitions to hold common, history‐independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta–Vohra analysis by allowing for history‐dependent expectations. The paper provides characterization results for two solution concepts that correspond to two versions of optimality. It demonstrates the power of history dependence by establishing nonemptyness results for all finite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions.

Tenses in 19th-century Dutch sentence-grammar

1988 ◽  
Vol 15 (1-2) ◽  
pp. 187-205
Author(s):  
J. A. Le Loux-Schuringa
Keyword(s):  
The Netherlands ◽  
19Th Century ◽  
Morphological Form ◽  
Other Information ◽  
Dutch Language ◽  
One To One ◽  
The 19Th Century ◽  
The Relationship

Summary In this paper some theories on tenses are described. These theories appeared in the Netherlands in the first half of the 19th century. The purpose is not just describing the different tense-systems of P. Weiland (1805), W. Bilderdijk (1826), W. G. Brill (1846) and L. A. te Winkel (1866). In the first half of the 19th century some fundamental changes took place. It is shown that these changes are based upon continuity of research of time and tense in the Dutch tradition. This continuity is found on three levels: (a) The research was concentrated on the verbal forms, no other information from the sentence was used. (b) The grammarians took the relationship between linguistic forms and logical categories as a one-to-one relation. (c) The morphological form of the Dutch language determined the grammatical representation of the tense-systems more and more.

scholarly journals Maximality in the Farsighted Stable Set

Econometrica ◽  
2019 ◽  
Vol 87 (5) ◽  
pp. 1763-1779 ◽  
Author(s):  
Debraj Ray ◽  
Rajiv Vohra
Keyword(s):  
Stable Set ◽  
Stable Sets ◽  
Von Neumann

Harsanyi (1974) and Ray and Vohra (2015) extended the stable set of von Neumann and Morgenstern to impose farsighted credibility on coalitional deviations. But the resulting farsighted stable set suffers from a conceptual drawback: while coalitional moves improve on existing outcomes, coalitions might do even better by moving elsewhere. Or other coalitions might intervene to impose their favored moves. We show that every farsighted stable set satisfying some reasonable and easily verifiable properties is unaffected by the imposition of these stringent maximality constraints. The properties we describe are satisfied by many, but not all, farsighted stable sets.

An Empirical Study of the use of EDI in Supermarket Chains using a New Conceptual Framework

1999 ◽  
Vol 14 (1) ◽  
pp. 3-21 ◽  
Author(s):  
Colm Fearon ◽  
George Philip
Keyword(s):  
Conceptual Framework ◽  
Electronic Data Interchange ◽  
Medium Size ◽  
Senior Managers ◽  
Self Assessment ◽  
Data Interchange ◽  
Electronic Transactions ◽  
Other Information ◽  
Expected Benefits ◽  
Almost All

Electronic Data Interchange (EDI) is now widely established as an interorganizational system in almost all large and medium size industrial, service and retail sectors and the purpose of this paper is to discuss the experiences of six supermarket chains concerning the use of this technology. Whilst the advantages of conducting electronic transactions are generally recognized, consensus on methodologies for quantifying the benefit success associated with interorganizational systems still remain elusive. It is argued that a comparison of pre-implementation expected benefits with post-implementation realized benefits can offer a reliable way of assessing the benefit success from EDI and other information systems. In this approach, the benefit success is expressed as a function of three benefit states namely, efficiency, neutrality and deficiency depending on whether the gap between realized and expected benefits is positive, neutral or negative respectively. In order to identify the benefit state of each participating organization, initially a series of semistructured interviews was conducted with senior managers followed by the administration of a self assessment rating instrument in the form of a questionnaire. This paper will discuss the findings along with the testing of a new conceptual framework for examining the relationship between benefit success, implementation approach and implementation success.

scholarly journals On the endomorphism near-ring of a free group

1980 ◽  
Vol 23 (1) ◽  
pp. 103-121 ◽  
Author(s):  
R. Warwick Zeamer
Keyword(s):  
Wreath Product ◽  
Free Group ◽  
The Other ◽  
Finite Support ◽  
Finite Product ◽  
Prime Factorization ◽  
Infinite Rank ◽  
One To One ◽  
Almost All ◽  
Countably Infinite

Suppose F is an additively written free group of countably infinite rank with basis T and let E = End(F). If we add endomorphisms pointwise on T and multiply them by map composition, E becomes a near-ring. In her paper “On Varieties of Groups and their Associated Near Rings” Hanna Neumann studied the sub-near-ring of E consisting of the endomorphisms of F of finite support, that is, those endomorphisms taking almost all of the elements of T to zero. She called this near-ring Φω. Now it happens that the ideals of Φω are in one to one correspondence with varieties of groups. Moreover this correspondence is a monoid isomorphism where the ideals of φω are multiplied pointwise. The aim of Neumann's paper was to use this isomorphism to show that any variety can be written uniquely as a finite product of primes, and it was in this near-ring theoretic context that this problem was first raised. She succeeded in showing that the left cancellation law holds for varieties (namely, U(V) = U′(V) implies U = U′) and that any variety can be written as a finite product of primes. The other cancellation law proved intractable. Later, unique prime factorization of varieties was proved by Neumann, Neumann and Neumann, in (7). A concise proof using these same wreath product techniques was also given in H. Neumann's book (6). These proofs, however, bear no relation to the original near-ring theoretic statement of the problem.

scholarly journals An existence theorem for abstract stable sets

1991 ◽  
Vol 51 (3) ◽  
pp. 468-472 ◽  
Author(s):  
Chih Chang ◽  
Gerard J. Chang
Keyword(s):  
Existence Theorem ◽  
Dominance Relation ◽  
Stable Set ◽  
Stable Sets

AbstractWe provide an existence theorem for stable sets which is equivalent to Zorn's lemma and study the connections between the unique stable set for majorization and the stable sets for the dominance relation.

scholarly journals VERY WELL-COVERED GRAPHS OF GIRTH AT LEAST FOUR AND LOCAL MAXIMUM STABLE SET GREEDOIDS

2011 ◽  
Vol 03 (02) ◽  
pp. 245-252 ◽  
Author(s):  
VADIM E. LEVIT ◽  
EUGEN MANDRESCU
Keyword(s):  
Perfect Matching ◽  
Local Maximum ◽  
Stable Set ◽  
Stable Sets ◽  
Maximum Cardinality ◽  
Math Program ◽  
The Family ◽  
Maximum Stable Set ◽  
Vertex Set ◽  
Appl Math

A maximum stable set in a graph G is a stable set of maximum cardinality. S is a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S. Nemhauser and Trotter Jr. [Vertex packings: structural properties and algorithms, Math. Program.8 (1975) 232–248], proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G. In [Levit and Mandrescu, A new greedoid: the family of local maximum stable sets of a forest, Discrete Appl. Math.124 (2002) 91–101] we have shown that the family Ψ(T) of a forest T forms a greedoid on its vertex set. The cases where G is bipartite, triangle-free, well-covered, while Ψ(G) is a greedoid, were analyzed in [Levit and Mandrescu, Local maximum stable sets in bipartite graphs with uniquely restricted maximum matchings, Discrete Appl. Math.132 (2004) 163–174], [Levit and Mandrescu, Triangle-free graphs with uniquely restricted maximum matchings and their corresponding greedoids, Discrete Appl. Math.155 (2007) 2414–2425], [Levit and Mandrescu, Well-covered graphs and greedoids, Proc. 14th Computing: The Australasian Theory Symp. (CATS2008), Wollongong, NSW, Conferences in Research and Practice in Information Technology, Vol. 77 (2008) 89–94], respectively. In this paper we demonstrate that if G is a very well-covered graph of girth ≥4, then the family Ψ(G) is a greedoid if and only if G has a unique perfect matching.

scholarly journals Pemberdayaan Perangkat Desa Terampil Bermedia dalam Membangun Kesadaran dan Kepedulian Masyarakat terhadap Lingkungan di Desa Cikeruh Kecamatan Jatinangor Kabupaten Sumedang

2019 ◽  
Vol 1 (2) ◽  
pp. 66
Author(s):  
Feliza Zubair ◽  
Iriana Bakti ◽  
Yustikasari Yustikasari
Keyword(s):  
Social Media ◽  
Community Service ◽  
Public Awareness ◽  
Regional Government ◽  
Research Activities ◽  
Other Information ◽  
Village Government ◽  
Use Of Social Media ◽  
Almost All ◽  
The Village

The Empowerment of Skilled-Media Village Officials in Building Public Awareness and Concern for the Environment in Cikeruh Village, Jatinangor District, Sumedang Regency The village government staff is the spearhead of the village government duty whose job is to deliver and process various information relating to government programs, both central and regional government. In this digital era, almost all information flow is carried out through social media. For this reason, a skilled and capable village government staff is needed, especially in using and utilizing social media devices. Through social media, the village government able to socialize the government's relay program and other information to residents. The village service of Cikeruh village through media social has not run optimally. Therefore, training in managing social media, especially in the socialization of environmental hygiene issues, must be held. Universitas Padjadjaran is one of the higher education institutions holding the mandate of community service through education and research activities. This community service integrated with student work college was held in Cikeruh village, Jatinangor District, Sumedang Regency. The training method was lecture and discussion methods, as well as hands-on practice. Participants gained various knowledge related to message management and the use of social media, especially Facebook and Instagram. The results of the activity were the increasing of the knowing, attitudes, and behavior of participants in using Instagram and Facebook to increase effort in improving and restructuring the environment in Cikeruh Village.

scholarly journals Greedoids on vertex sets of B-joins of graphs

2014 ◽  
Vol 30 (3) ◽  
pp. 335-344
Author(s):  
VADIM E. LEVIT ◽  
◽  
EUGEN MANDRESCU ◽  
Keyword(s):  
Bipartite Graph ◽  
Sufficient Conditions ◽  
Local Maximum ◽  
Stable Set ◽  
Stable Sets ◽  
The Family ◽  
Maximum Stable Set ◽  
Vertex Set ◽  
Necessary And Sufficient ◽  
Vertex Sets

Let Ψ(G) be the family of all local maximum stable sets of graph G, i.e., S ∈ Ψ(G) if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S. It was shown that Ψ(G) is a greedoid for every forest G [15]. The cases of bipartite graphs, triangle-free graphs, and well-covered graphs, were analyzed in [16, 17, 18, 19, 20, 24]. If G1, G2 are two disjoint graphs, and B is a bipartite graph having E(B) as an edge set and bipartition {V (G1), V (G2)}, then by B-join of G1, G2 we mean the graph B (G1, G2) whose vertex set is V (G1) ∪ V (G2) and edge set is E(G1) ∪ E(G2) ∪ E (B). In this paper we present several necessary and sufficient conditions for Ψ(B (G1, G2)) to form a greedoid, an antimatroid, and a matroid, in terms of Ψ(G1), Ψ(G2) and E (B).

scholarly journals Stable sets of weak tournaments

2004 ◽  
Vol 14 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Somdeb Lahiri
Keyword(s):  
Stable Set ◽  
Stable Sets ◽  
Empty Subset

In this paper we obtain conditions on weak tournaments, which guarantee that every non-empty subset of alternatives admits a stable set. We also show that there exists a unique stable set for each non-empty subset of alternatives which coincides with its set of best elements, if and only if, the weak tournament is quasi-transitive. A somewhat weaker version of this result, which is also established in this paper, is that there exists a unique stable set for each non-empty subset of alternatives (: which may or may not coincide with its set of best elements), if and only if the weak tournament is acyclic.

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