This piece in the Milestones series is dedicated to paper coauthored by David Gale and Lloyd Shapley published 1962 under title “College admissions stability of marriage” on American Mathematical Monthly.

We investigate the state space of bipartite qutrits. For states which are locally maximally mixed we obtain an analog of the “magic” tetrahedron for bipartite qubits—a magic simplex W. This is obtained via the Weyl group which is a kind of “quantization” of classical phase space. We analyze how this simplex W is embedded in the whole state space of two qutrits and discuss symmetries and equival...

At CT-RSA 2009, a new principle to secure RSA (and modular/group exponentiation) against fault-analysis has been introduced by Rivain. The idea is to perform a so-called double exponentiation to compute a pair (md,mφ(N)−d) and then check that the output pair satisfies the consistency relation: m ·mφ(N)−d ≡ 1 mod N . The author then proposed an efficient heuristic to derive an addition chain for...

We construct orthogonal double covers of Kn,n by Pm+1 ∪∗ Sn−m, where n and m are integers, 2 ≤ m ≤ 10, m ≤ n and Pm+1 ∪∗ Sn−m is a tree obtained from the path Pm+1 with m edges and a star Sn−m with n − m edges by identifying an end-vertex of Pm+1 with the center of Sn−m.

Group testing is the problem to identify up to d defectives out of n elements, by testing subsets for the presence of defectives. Let t(n, d, s) be the optimal number of tests needed by an s-stage strategy in the strict group testing model where the searcher must also verify that at most d defectives are present. We start building a combinatorial theory of strict group testing. We compute many ...

In a recent paper [9], the authors introduced the extended Q-bipartite double of an almost dual bipartite cometric association scheme. Since the association schemes arising from linked systems of symmetric designs are almost dual bipartite, this gives rise to a new infinite family of 4-class cometric schemes which are both Q-bipartite and Q-antipodal. These schemes, the schemes arising from lin...

Robertson and Seymour proved that every graph with sufficiently large treewidth contains a large grid minor. However, the best known bound on the treewidth that forces an l × l grid minor is exponential in l. It is unknown whether polynomial treewidth suffices. We prove a result in this direction. A grid-like-minor of order l in a graph G is a set of paths in G whose intersection graph is bipar...

for a graph g, let d(g) be the set of all strong orientations of g. the orientationnumber of g is min {d(d) |d belongs to d(g)}, where d(d) denotes the diameterof the digraph d. in this paper, we determine the orientation number for some subgraphs of complete bipartite graphs.

Robertson and Seymour proved that every graph with sufficiently large treewidth contains a large grid minor. However, the best known bound on the treewidth that forces an l × l grid minor is exponential in l. It is unknown whether polynomial treewidth suffices. We prove a result in this direction. A grid-like-minor of order l in a graph G is a set of paths in G whose intersection graph is bipar...