Locally Convex Words and Permutations

Locally Convex Words and Permutations

We introduce some new classes of words and permutations characterized by the second difference condition π(i − 1) + π(i + 1) − 2π(i) ≤ k, which we call the k-convexity condition. We demonstrate that for any sized alphabet and convexity parameter k, we may find a generating function which counts k-convex words of length n. We also determine a formula for the number of 0-convex words on any fixed...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

On convex permutations

A selection of points drawn from a convex polygon, no two with the same vertical or horizontal coordinate, yields a permutation in a canonical fashion. We characterise and enumerate those permutations which arise in this manner and exhibit some interesting structural properties of the permutation class they form. We conclude with a permutation analogue of the celebrated Happy Ending Problem. 1 ...

Permutations Defining Convex Permutominoes

A permutomino of size n is a polyomino determined by particular pairs (π1, π2) of permutations of size n, such that π1(i) 6= π2(i), for 1 ≤ i ≤ n. Here we determine