On decomposition of sub-linearised polynomials

We give a detailed exposition of the theory of decompositions of linearised polynomials, using a well-known connection with skew-polynomial rings with zero derivative. It is known that there is a one-to-one correspondence between decompositions of linearised polynomials and sub-linearised polynomials. This correspondence leads to a formula for the number of indecomposable sub-linearised polynomials of given degree over a finite field. We also show how to extend existing factorisation algorithms over skew-polynomial rings to decompose sub-linearised polynomials without asymptotic cost.

Equity market linkage and multinational trade accords: The case of NAFTA

This paper examines the impact of multinational trade accords on the degree of stock market linkage using NAFTA as a case study. Besides liberalizing trade among the U.S., Canada and Mexico, NAFTA has also sought to strengthen linkage among stock markets of these countries. If successful, this could lessen the appeal of asset diversification across the North American region and promote a higher degree of market efficiency. We assess the possible impact of NAFTA on market linkage using cross-correlations, multivariate price cointegrating systems, speed of convergence, and generalized variance decompositions of unexpected stock returns. The evidence proves robust and consistently indicates intensified equity market linkage since the NAFTA accord. The results also suggest that interdependent goods markets in the region are a primary reason behind the stronger equity market linkage observed in the post-NAFTA period. (c) 2005 Elsevier Ltd. All rights reserved.

Packing lambda-fold complete multipartite graphs with 4-cycles

A maximum packing of any lambda-fold complete multipartite graph (where there are lambda edges between any two vertices in different parts) with edge-disjoint 4- cycles is obtained and the size of each minimum leave is given. Moreover, when lambda =2, maximum 4-cycle packings are found for all possible leaves.

Steiner triple systems with two disjoint subsystems

It is shown that there exists a triangle decomposition of the graph obtained from the complete graph of order v by removing the edges of two vertex disjoint complete subgraphs of orders u and w if and only if u, w, and v are odd, ((v)(2)) - ((u)(2)) - ((w)(2)) equivalent to 0 (mod 3), and v >= w + u + max {u, w}. Such decompositions are equivalent to group divisible designs with block size 3, one group of size u, one group of size w, and v - u - w groups of size 1. This result settles the existence problem for Steiner triple systems having two disjoint specified subsystems, thereby generalizing the well-known theorem of Doyen and Wilson on the existence of Steiner triple systems with a single specified subsystem. (c) 2005 Wiley Periodicals, Inc.