EJC
2010
13 years 4 months ago
2010
Mutually unbiased bases (MUBs) in complex vector spaces play several important roles in quantum information theory. At present, even the most elementary questions concerning the m...
EJC
2010
13 years 4 months ago
2010
EJC
2010
13 years 4 months ago
2010
A Shilla distance-regular graph (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divide...
EJC
2010
13 years 4 months ago
2010
We study two enumeration problems for up-down alternating trees, i.e., rooted labelled trees T, where the labels v1, v2, v3, . . . on every path starting at the root of T satisfy v...
EJC
2010
13 years 4 months ago
2010
We start by describing all the varieties of loops Q that can be defined by autotopisms x, x Q, where x is a composition of two triples, each of which becomes an autotopism when th...
EJC
2010
13 years 4 months ago
2010
Each clone C on a fixed base set A determines a quasiorder on the set of all operations on A by the following rule: f is a C-minor of g if f can be obtained by substituting operati...
EJC
2010
13 years 4 months ago
2010
Abstract. We prove that the combinatorial distance between any two reduced expressions of a given permutation of {1, ..., n} in terms of transpositions lies in O(n4), a sharp bound...
EJC
2010
13 years 4 months ago
2010
We consider the number of nodes in the levels of unlabelled rooted random trees and show that the stochastic process given by the properly scaled level sizes weakly converges to th...
EJC
2010
13 years 4 months ago
2010
In this paper, we investigate some properties of partial covers of PG(n, q). We show that a set of q + a hyperplanes, q 81, a < (q - 1)/3, or q > 13 and a (q - 10)/4, that...
EJC
2010
13 years 4 months ago
2010
A classical result of Euler states that the tangent numbers are an alternating sum of Eulerian numbers. A dual result of Roselle states that the secant numbers can be obtained by a...