We study the derangement number on a Ferrers board B = (n × n) − λ with respect to an initial permutation M , that is, the number of permutations on B that share no common points with M . We prove that the derangement number is independent of M if and only if λ is of rectangular shape. We characterize the initial permutations that give the minimal and maximal derangement numbers for a general F...

General methods for the determination of maximal finite absolutely irreducible subgroups of GL(n, Z) are described. For n = 5, 7 all these groups are computed up to Z-equivalence.

We prove Heden’s result that the deficiency δ of a maximal partial spread in PG(3, q) is greater than 1+ 1 2 (1+ √ 5)q unless δ−1 is a multiple of p, where q = p. When q is odd and not a square, we are able to improve this lower bound to roughly √ 3q.

Let (W,S) be an arbitrary Coxeter system. For each sequence ω = (ω1, ω2, . . .) ∈ S∗ in the generators we define a partial order—called the ω-sorting order—on the set of group elements Wω ⊆ W that occur as finite subwords of ω. We show that the ω-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and strong Bruhat orders on the group. Moreover, t...

Experiential learning activities (ELAs) that are industry-partnered and real-world problem-based can provide undergraduate students with concrete experiences of using information technologies in the field. Flow theory provides a theoretical basis to guide the design of ELAs, ensuring that the goals are clear, feedback is explicit, and the challenges and skills are balanced. Based on this theory...

Let A be a non singleton finite set. We show that every maximal clone determined by a prime affine or h-universal relation on A is contained in a family of partial clones on A of continuum cardinality. MSC 2000: 03B50, 08A40, 08A55

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, then the uniform allocation rule is the unique strategy-proof, efficient, and anonymous rule. We identify the maximal set of preferences, containing the set of single-peaked preferences, under which...

Let G ' Z/k1Z⊕ · · · ⊕ Z/kNZ be a finite abelian group with ki|ki−1 (2 ≤ i ≤ N). For a matrix Y = ( ai,j ) ∈ ZR×S satisfying ai,1 + · · ·+ ai,S = 0 (1 ≤ i ≤ R), let DY (G) denote the maximal cardinality of a set A ⊆ G for which the equations ai,1x1 + · · · + ai,SxS = 0 (1 ≤ i ≤ R) are never satisfied simultaneously by distinct elements x1, . . . , xS ∈ A. Under certain assumptions on Y and G, w...

We prove an inequality of the form γn ≥ Cn(γn−1) between Hermite’s constants γn and γn−1. This inequality yields also a new proof of the Minkowski-Hlawka bound ∆n ≥ ζ(n)21−n for the maximal density ∆n of n−dimensional lattice-packings. 1

Consider a compact locally symmetric space M of rank r, with fundamental group Γ. The von Neumann algebra VN(Γ) is the convolution algebra of functions f ∈ l2(Γ) which act by left convolution on l2(Γ). Let T r be a totally geodesic flat torus of dimension r in M and let Γ0 ∼= Z r be the image of the fundamental group of T r in Γ. Then VN(Γ0) is a maximal abelian ⋆-subalgebra of VN(Γ) and its un...