Poset pattern-avoidance problems posed by Yakoubov

New problems of pattern avoidance

The Dyck pattern poset

We introduce the notion of pattern in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck paths, which we call the Dyck pattern poset. Given a Dyck path P , we determine a formula for the number of Dyck paths covered by P , as well as for the ...

Pattern avoidance by palindromes

We show that every avoidable pattern can be avoided by an infinite sequence of palindromes over a fixed finite alphabet. © 2009 Elsevier B.V. All rights reserved.

Ill-Posed and Linear Inverse Problems

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

On Poset Sandwich Problems

A graph Gs = (V,Es) is a sandwich for a pair of graph Gt = (V,Et) and G = (V,E) if Et ⊆ Es ⊆ E. Any poset, or partially ordered set, admits a unique graph representation which is directed and transitive. In this paper we introduce the notion of sandwich poset problems inspired by former sandwich problems on comparability graphs. In particular, we are interested in seriesparallel and interval po...