!Istituto Chimica Tecnologia Prodotti Naturali, C.N.R. (associated with Istituto Nazionale Chimica Sistemi Biologici, C.N.R.), 153 La Malfa, 90146 Palermo, Italy "Science Exact Institute, Chemistry Department, Oum El Bouaghi University, Oum El Bouaghi 04000, Algeria #Dipartimento Chimica Organica, Universita% Palermo, Viale d.Scienze, 90128 Palermo, Italy $Jodrell Laboratory, Royal Botanic Gard...

Given a property P of graphs, write P for the set of graphs with vertex set [n] having property P. The growth or speed of a property P can be discussed in terms of the values of |P|. For properties with |P|<n hereditary properties are surprisingly well determined by their speeds. Sharpening results of E. R. Scheinerman and J. Zito (1994, J. Combin. Theory Ser. B 61, 16 39), we prove numerous re...

We use a variety of combinatorial techniques to prove several theorems concerning fractional dimension of partially ordered sets. In particular, we settle a conjecture of Brightwell and Scheinerman by showing that the fractional dimension of a poset is never more than the maximum degree plus one. Furthermore, when the maximum degree k is at least two, we show that equality holds if and only if ...

The Argentinian author Silvina Ocampo (1903-1993) left us a vast body of works which are considered outstanding in many ways. In 1960, she published a short story, entitled "El médico encantador" (The Charming Physician), in the renowned literary magazine Sur. The central character of this piece is a family doctor named Albino Morgan, who had a secret truth: in any house he visited, all variety...

Karel Souček, Andrés Kamaid, Anh D. Phung, Lukáš Kubala, J. Chloë Bulinski, Richart W. Harper, and Jason P. Eiserich* Departmentof InternalMedicine,Universityof California,Davis,California Departmentof PhysiologyandMembrane Biology,Universityof California,Davis,California Cancer Center, SchoolofMedicine,Universityof California,Davis,California Departmentof Biological Sciencesand PathologyandCel...

Thank you very much Dean. I am delighted to be back at the Law School this afternoon. As I look around the room, I see people from my past and present. I was a student of Professor Gorman and Professor Lesnick in the early 1970s. A few years later, I worked with individuals who are in the audience from the State Department of Education in Harrisburg. Richard Mandell' was part of the interviewin...

A more sums than differences (MSTD) set is a finite subset S of the integers such that |S + S| > |S − S|. We construct a new dense family of MSTD subsets of {0, 1, 2, . . . , n − 1}. Our construction gives Θ(2n/n) MSTD sets, improving the previous best construction with Ω(2/n) MSTD sets by Miller, Orosz, and Scheinerman.

When the random intersection graph G(n,m, p) proposed by Karoński, Scheinerman, and Singer-Cohen in [8] is compared with the independent-edge G(n, p), the evolutions are different under some values of m and equivalent under others. In particular, when m = nα and α > 6, the total variation distance between the graph random variables has limit 0.

In 1971 Trotter (or Bogart and Trotter) conjectured that every finite poset on at least 3 points has a pair whose removal does not decrease the dimension by more than 1. In 1992 Brightwell and Scheinerman introduced fractional dimension of posets, and they made a similar conjecture for fractional dimension. This paper settles this latter conjecture.