Branchwidth is a connectivity parameter of graphs closely related to treewidth. Graphs of treewidth at most k can be generated algorithmically as the subgraphs of k-trees. In this paper, we investigate the family of edge-maximal graphs of branchwidth k, that we call k-branches. The k-branches are, just as the k-trees, a subclass of the chordal graphs where all minimal separators have size k. Ho...

  We consider the maximal covering location-allocation problem with multiple servers. The objective is to maximize the population covered, subject to constraints on the number of service centers, total number of servers in all centers, and the average waiting time at each center. Each center operates as an M/M/k queuing system with variable number of servers. The total costs of establishing cen...

This note provides a specific quiver which does not admit a maximal green sequence, and which is mutation-equivalent to a quiver which does admit a maximal green sequence. This provides a counterexample to the conjecture that the existence of maximal green sequences is invariant under quiver mutation. The proof uses the ‘scattering diagrams’ of Gross-Hacking-Keel-Kontsevich to show that a maxim...

In 1975, Lovász conjectured that any maximal intersecting family of k-sets has at most b(e− 1)k!c blocks, where e is the base of the natural logarithm. This conjecture was disproved in 1996 by Frankl and his co-authors. In this short note, we reprove the result of Frankl et al. using a vastly simplified construction of maximal intersecting families with many blocks. This construction yields a m...

Exercise 1 (Maximal compact subgroups of G). A lattice in Qp is a finitelygenerated Zp-submodule of Qp that generates Qp as vector space. In particular, it’s free of rank n. Note that G acts transitively on the set of lattices in Qp . (i) Show that K = StabG(Zp ). (ii) Suppose that K ′ is a compact subgroup of G. Show that K ′ stabilises a lattice. (Hint: show that the K ′-orbit of Zp is finite...

Let X; X 1 ; : : : ; X k be i.i.d. random variables, and for k 2 IN let D k (X) = E(X 1 _ _ X k+1) ? EX be the k-th centralized maximal moment. A sharp lower bound is given for D 1 (X) in terms of the L evy concentration Q l (X) = sup x2IR P (X 2 x; x + l]). This inequality, which is analogous to P. L evy's concentration-variance inequality, illustrates the fact that maximal moments are a gauge...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

There are strong analogies between groups definable in o-minimal structures and real Lie groups. Nevertheless, unlike the real case, not every definable group has maximal definably compact subgroups. We study definable groups G which are not definably compact showing that they have a unique maximal normal definable torsion-free subgroup N ; the quotient G/N always has maximal definably compact ...