scholarly journals Determining a Binary Matroid from its Small Circuits

10.37236/5373 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
James Oxley ◽  
Charles Semple ◽  
Geoff Whittle
Keyword(s):  
Binary Matroid ◽  
Special Restriction

It is well known that a rank-$r$ matroid $M$ is uniquely determined by its circuits of size at most $r$. This paper proves that if $M$ is binary and $r\ge 3$, then $M$ is uniquely determined by its circuits of size at most $r-1$ unless $M$ is a binary spike or a special restriction thereof. In the exceptional cases, $M$ is determined up to isomorphism.

scholarly journals On Binary Matroid Minors and Applications to Data Storage over Small Fields

2017 ◽  
pp. 139-153
Author(s):  
Matthias Grezet ◽  
Ragnar Freij-Hollanti ◽  
Thomas Westerbäck ◽  
Camilla Hollanti
Keyword(s):  
Data Storage ◽  
Binary Matroid ◽  
Small Fields

The Construction of Racial Difference in Twentieth-Century Britain: The Special Restriction (Coloured Alien Seamen) Order, 1925

1994 ◽  
Vol 33 (1) ◽  
pp. 54-98 ◽  
Author(s):  
Laura Tabili
Keyword(s):  
Social Relations ◽  
Racial Difference ◽  
British Society ◽  
Power Dynamics ◽  
Historical Contingency ◽  
Sexual Competition ◽  
Black And White ◽  
Working People ◽  
Special Restriction ◽  
History Of

In the course of the past several decades, scholars have exposed Black people's long history of life and work in Britain, but their approaches to racial conflict have slighted the historical contingency of racial difference itself. Black workers have been presented as logical, visible scapegoats in an otherwise homogeneous working class, and interracial hostility as an ineluctable product of economic or sexual competition between two mutually exclusive and naturally antagonistic groups of working men. Scholars examining Black people's experience in Britain under the rubric “immigrants and minorities” have placed particular emphasis on racial conflicts, xenophobia, and prejudice, which they see as evidence of “traditions of intolerance” widespread in British society. Such interpretations leave unchallenged the assumption that racial or ethnic hostility is latent in social relations, resurfacing in any crisis. Whatever the intentions of their authors, such assumptions can all too easily be used to justify rather than to combat conflict and exclusion.Intolerance, bigotry, prejudice, moreover, are not explanations for racial or ethnic conflict: in themselves they require explanation. In focusing on “attitudes,” and behaviors, these works neglect to examine the structural underpinnings of popular racism and xenophobia—in particular the ways that Black and white working people were positioned in relation to each other within a system also riven by class, gender, skill, and other power dynamics. What many scholars have taken for granted, indeed, is the objective or fixed quality of racial difference itself and its inexorably divisive effects.

Reconsidering Some Passages in Wittgenstein

1971 ◽  
Vol 2 (1) ◽  
pp. 1-28
Author(s):  
Frank B. Ebersole
Keyword(s):  
Common Property ◽  
Blue Book ◽  
Philosophical Investigations ◽  
Common Features ◽  
Family Resemblances ◽  
Special Restriction ◽  
Word Feature

I want to consider some difficulties which I have on rereading the passages on “common properties” or “common features” and “family resemblances” in The Blue Book (p. 17) and in Philosophical Investigations (§65 - §71 ). These passages are not as easy to read as they once were. Wittgenstein tells us that we think, or have a tendency to think, that all the things to which we apply a general word have some property or feature in common, and he tells us that we believe it is because of this common property or feature that we apply the same word to them. In The Blue Book the phrase is “common property”; in Philosophical Investigations it is “common feature.” Wittgenstein may have changed from the word “property” to the word “feature” because the word “property” is obviously too limited in its application. We speak of the properties of mercury or neoprene but not of the properties of barnowls or slatterns. The word “feature” also seems too limited in a way, but he may have chosen this word mainly because it fits his metaphor of family resemblances. I do not think that Wittgenstein wants to impose any special restriction at this point, so I shall use the word “feature” only where it is appropriate, and I shall use the less limiting word “characteristic” where it seems more appropriate than the word “feature.” Thus I assume that Wittgenstein means to examine our tendency to think that a general word is applied to things because those things have some features or features, characteristic or characteristics in common.

A characterization of n-connected splitting matroids

2014 ◽  
Vol 07 (04) ◽  
pp. 1450060
Author(s):  
P. P. Malavadkar ◽  
M. M. Shikare ◽  
S. B. Dhotre
Keyword(s):  
Binary Matroid ◽  
Binary Matroids ◽  
Splitting Operation

The splitting operation on an n-connected binary matroid may not yield an n-connected binary matroid. In this paper, we characterize n-connected binary matroids which yield n-connected binary matroids by the generalized splitting operation.

scholarly journals Splitting in a binary matroid

1998 ◽  
Vol 184 (1-3) ◽  
pp. 267-271 ◽  
Author(s):  
T.T. Raghunathan ◽  
M.M. Shikare ◽  
B.N. Waphare
Keyword(s):  
Binary Matroid

scholarly journals 28. Some Problems Concerning the So-Called Survivors of the Yin Dynasty

Early China ◽  
1986 ◽  
Vol 9 (S1) ◽  
pp. 58-60
Author(s):  
Tu Cheng-Sheng
Keyword(s):  
The State ◽  
Basic Error ◽  
Literary Sources ◽  
Bronze Vessels ◽  
Special Restriction ◽  
History Of ◽  
Close Relatives ◽  
Seven Generations ◽  
High Social Status ◽  
Primary Unit

ABSTRACTThe basic error in Hu Shi's “An Exposition on Confucians” lay in discussing the basic nature of the Confucian school on the basis of the “tragic fate and miserable status of the survivors of the Shang”; for half a century this mistaken premise has been accepted by most historians as proven. On the basis of an analysis of pre-Qin literary sources, this paper first proves that there was no “tragedy of the defeated state”; on the contrary, the Yin survivors continued to possess considerable political power and quite high social status. Second, on the basis of newly un earthed Shang and Zhou inscriptions, the fate and status of the Shang survivors is set forth from three sides: (1) The history of the Wei Shi clan and Lu Sheng clan of the Guanzhong region, for which genealogies of seven-eight or six-seven generations exist, is reconstructed on the basis of, for the former, the Ding bronze horde newly unearthed from Fufeng Zhuangbai, and, for the latter, the inscriptions on already known as well as recently unearthed bronze vessels from the same area. Both clans were survivors from the Shang and close relatives of the Shang king; they possessed cities, subjects, and official positions, as well as holding offices in charge of troops. (2) The same conclusion may be reached in individual cases in various other kingdoms, such as for Mo Situ Sung of the state of Wei , and Dong Hefu of the state of Yan . As for the Ling Shi , Chen Chen and Deng of Cheng Zhou , Cheng Zhou is the ancient home of the Shang survivors, yet they seem not to have been the object of any special restriction or suppression. This section is based solely on inscriptions; the conclusions reached, however, are completely in agreement with those derived from literary evidence in the previous section. Finally an attempt is made to explain why the survivors of the Shang had land, subjects, offices, and power. We believe that it was due to a political and social structure with the clan as the primary unit. A complete explication of this question awaits a detailed study of oracle-bone and archaeological source material.

scholarly journals Quasiregular Matroids

10.37236/6911 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
S. R. Kingan
Keyword(s):  
The Self ◽  
Binary Matroid ◽  
Binary Matroids

Regular matroids are binary matroids with no minors isomorphic to the Fano matroid $F_7$ or its dual $F_7^*$. Seymour proved that 3-connected regular matroids are either graphs, cographs, or $R_{10}$, or else can be decomposed along a non-minimal exact 3-separation induced by $R_{12}$. Quasiregular matroids are binary matroids with no minor isomorphic to the self-dual binary matroid $E_4$. The class of quasiregular matroids properly contains the class of regular matroids. We prove that 3-connected quasiregular matroids are either graphs, cographs, or deletion-minors of $PG(3,2)$, $R_{17}$ or $M_{12}$ or else can be decomposed along a non-minimal exact 3-separation induced by $R_{12}$, $P_9$, or $P_9^*$.

scholarly journals Playing Nim on a Simplicial Complex

10.37236/1233 ◽  
1996 ◽  
Vol 3 (1) ◽  
Author(s):  
Richard Ehrenborg ◽  
Einar Steingrímsson
Keyword(s):  
Simplicial Complex ◽  
Winning Strategy ◽  
Independent Sets ◽  
Binary Matroid ◽  
Classical Game

We introduce a generalization of the classical game of Nim by placing the piles on the vertices of a simplicial complex and allowing a move to affect the piles on any set of vertices that forms a face of the complex. Under certain conditions on the complex we present a winning strategy. These conditions are satisfied, for instance, when the simplicial complex consists of the independent sets of a binary matroid. Moreover, we study four operations on a simplicial complex under which games on the complex behave nicely. We also consider particular complexes that correspond to natural generalizations of classical Nim.

scholarly journals A Characterization of Circle Graphs in Terms of Multimatroid Representations

10.37236/6992 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Robert Brijder ◽  
Lorenzo Traldi
Keyword(s):  
Simple Graph ◽  
Rank Function ◽  
Binary Matroid ◽  
Circle Graph ◽  
Circle Graphs ◽  
Isotropic System

The isotropic matroid $M[IAS(G)]$ of a looped simple graph $G$ is a binary matroid equivalent to the isotropic system of $G$. In general, $M[IAS(G)]$ is not regular, so it cannot be represented over fields of characteristic $\neq 2$. The ground set of $M[IAS(G)]$ is denoted $W(G)$; it is partitioned into 3-element subsets corresponding to the vertices of $G$. When the rank function of $M[IAS(G)]$ is restricted to subtransversals of this partition, the resulting structure is a multimatroid denoted $\mathcal{Z}_{3}(G)$. In this paper we prove that $G$ is a circle graph if and only if for every field $\mathbb{F}$, there is an $\mathbb{F}$-representable matroid with ground set $W(G)$, which defines $\mathcal{Z}_{3}(G)$ by restriction. We connect this characterization with several other circle graph characterizations that have appeared in the literature.

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