This paper studies structural aspects of lattice path matroids, a class of transversal matroids that is closed under taking minors and duals. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats. One of the main results is a characterization of lattice path matroids in terms of fundamental flats, which are special connected flats from which one can recove...

Sex offenders have used the Internet to identify and contact minors for sexual exploitation (Armagh, 1998; Hernandez, 2000; Lamb, 1998; Lanning, 1998). Yet little is known about how these individuals select their online victims. In order to gain a better understanding of this behavior, the online activity of 31 men who perpetrated or attempted to perpetrate contact sex offenses against minors t...

A graph G is loosely-c-connected, or l-c-connected, if there exists a number d depending on G such that the deletion of fewer than c vertices from G leaves precisely one infinite component and a graph containing at most d vertices. In this paper, we give the structure of a set of l-c-connected infinite graphs that form an unavoidable set among the topological minors of l-c-connected infinite gr...

We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the nth and n−1th minors, whose solution is a representation of the nth minor as an n × n determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit ...

We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the nth and n−1th minors, whose solution is a representation of the nth minor as an n × n determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit ...

Oral cancer is second most common cancer in Pakistan and one of the major contributing factors to its high incidence is smokeless tobacco (SLT) use. 5.3% of Pakistan's youth are current SLT users. The World Health Organization requires the signatories of its "Framework Convention on Tobacco Control" to officially ban the sale of tobacco products to minors. We reviewed the Government of Pakistan...

It is well known that in finite graphs, large complete minors/topological minors can be forced by assuming a large average degree. Our aim is to extend this fact to infinite graphs. For this, we generalize the notion of the relative end degree, which had been previously introduced by the first author for locally finite graphs, and show that large minimum relative degree at the ends and large mi...

The mandatory reporting system for assaults against minors is an effective measure to timely detect and intervene in cases of assault. It has long been used by countries as important means protect minors. In 2020, China formally established the when nine ministries commissions issued "Opinions on Establishing a Mandatory Reporting System Cases Assault Minors (for Trial Implementation)" specifie...

We begin by giving some background to this result. A matroid M is an excluded minor for a minor-closed class of matroids if M is not in the class but all proper minors of M are. It is natural to attempt to characterize a minor-closed class of matroids by giving a complete list of its excluded minors. Unfortunately, a minor-closed class of matroids can have an infinite number of excluded minors....