Mathematics Commons^™

On The Topology Of The Permutation Pattern Poset, Peter R. W. Mcnamara, Einar Steingrímsson

Peter R. W. McNamara

Examining The Literature On “Networks In Space And In Time.” An Introduction, Luca De Benedictis, Prosperina Vitale, Stanley Wasserman

Luca De Benedictis

The Network science special issue of “Networks in space and in time: methods and applications” contributes to the debate on contextual analysis in network science. It includes seven research papers that shed light on the analysis of network phenomena studied within geographic space and across temporal dimensions. In these papers, methodological issues as well as specific applications are described from different fields. We take the seven papers, study their citations and texts, and relate them to the broader literature. By exploiting the bibliographic information and the textual data of these seven documents, citation analysis and lexical correspondence analysis allow us …

Comparing Skew Schur Functions: A Quasisymmetric Perspective, Peter R. W. Mcnamara

Peter R. W. McNamara

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions s_A and s_B are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that s_A and s_B have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true.

In fact, we work in terms of inequalities, showing that if the F-support of s_{A …}