This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal I+(C) to an arbitrary linear code. The binomials involved in the reduced Gröbner basis of such an ideal relative to a degreecompatible ordering induce a uniquely defined test-set for the code, and this allows the descript...

AND GENERIC RIGIDITY IN THE PLANE SACHIN PATKAR, BRIGITTE SERVATIUS, AND K. V. SUBRAHMANYAM Abstract. We consider the concept of abstract 2–dimensional rigidity and provide necessary and sufficient conditions for a matroid to be an abstract rigidity matroid of a complete graph. This characterization is a natural extenWe consider the concept of abstract 2–dimensional rigidity and provide necessa...

We study Graver test sets for families of linear multi-stage stochastic integer programs with varying number of scenarios. We show that these test sets can be decomposed into finitely many “building blocks”, independent of the number of scenarios, and we give an effective procedure to compute them. The paper includes an introduction to Nash-Williams’ theory of better-quasi-orderings, which is u...

We call a graph G = (V,E) a (k, `)-circuit if |E| = k|V | − ` + 1 and every X ⊂ V with 2 ≤ |X| ≤ |V | − 1 satisfies i(X) ≤ k|X| − `. A (2, 3)-circuit is also called a generic circuit. We say that a graph is balanced if the difference between its maximum and minimum degree is at most 1. J. Graver, B. Servatius and H. Servatius asked in [7] whether a balanced generic circuit always admits a decom...

Ascaridiasis shows no predilection for any sex or age, but the graver symptoms are usually encountered only in the young. From minor intestinal disorders to serious abdominal complications, e.g. intestinal obstruction, appendicitis, liver abscess, even perforation of the gut, all have found mention in textbooks. Ascaridiasis is known to produce complications in other organs as well, e.g. bronch...

SIMPLE open-angle glaucoma in the South African Bantu races is an even graver disease than in Europeans. Should the disease progress, as it usually does, so that drug therapy no longer controls the pressure and surgery becomes inevitable, the results of drainage operations -are strangled by the relatively rapid fibrosis that develops. Generally this has been attributed to the keloid tendency of...

Although it is commonly believed that immigration leads to a high crime rate, this relationship is far from conclusive. This paper contributes to this line of research by exploring the case of China, a country undergoing rapid and profound urbanization. We collected and analyzed the arrest and prosecution data from the procuratorates of 306 prefectures in China, combined with interviews with ni...