Excluded minors for the class of split matroids

The class of split matroids arises by putting conditions on the system of split hyperplanes of the matroid base polytope. It can alternatively be defined in terms of structural properties of the matroid. We use this structural description to give an excluded minor characterisation of the class

Kinser inequalities and related matroids

Kinser developed a hierarchy of inequalities dealing with the dimensions of certain spaces constructed from a given quantity of subspaces. These inequalities can be applied to the rank function of a matroid, a geometric object concerned with dependencies of subsets of a ground set. A matroid which is representable by a matrix with entries from some finite field must satisfy each of the Kinser inequalities. We provide results on the matroids which satisfy each inequality and the structure of the hierarchy of such matroids.Comment: 82 pages, 7 figures. MSc thesi

A lattice point counting generalisation of the Tutte polynomial

International audienceThe Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion- contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a matroid, and in fact contains the same information as the Tutte polynomial when we restrict to matroids. This polynomial is constructed using lattice point counts in the Minkowski sum of the base polytope of a polymatroid and scaled copies of the standard simplex. We also show that, in the matroid case, our polynomial has coefficients of alternating sign, with a combinatorial interpretation closely tied to the Dawson partition

Redesigning Stoddard Residence Hall

This project designed and analyzed a freshman dormitory building to replace the current Stoddard Hall. Objectives included increasing student capacity, building with existing contour of the land and satisfying students\u27 needs. These objectives were met through preliminary research, architectural layout, structural design and a series of cost estimates on areas such as atriums and masonry construction. Research was conducted into building codes, zoning ordinances and RS Means estimating. Structural work was focused on use of W-shape rolled steel for support

Examining CEFR-related Professional Learning Interventions for Language Teachers: A Qualitative Meta-synthesis

Current language teaching and learning reflects an increasingly situated approach, paralleling the tenets of the Common European Framework of Reference for languages (CEFR). Although these methods are promoted in language curricula globally, how language educators are being prepared to adopt these approaches is less clear. This project therefore sought to investigate how CEFR-related training interventions are being used internationally with second language (L2+) pre-service and in-service teachers. Here, we provide the results of a qualitative meta-synthesis of literature on professional learning on the CEFR. Seventeen studies met the final inclusion criteria. The existing literature demonstrates how explicit training on the CEFR can support teachers’ understanding and positive perception of the framework and align teachers’ planning, pedagogy, and assessment practices with contemporary tenets for language teaching and learning. These studies provide insights into the impact, opportunities, and challenges related to engaging L2 teachers in CEFR learning

Polytopal and structural aspects of matroids and related objects

PhDThis thesis consists of three self-contained but related parts. The rst is focussed on polymatroids, these being a natural generalisation of matroids. The Tutte polynomial is one of the most important and well-known graph polynomials, and also features prominently in matroid theory. It is however not directly applicable to polymatroids. For instance, deletion-contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a matroid, and in fact contains the same information as the Tutte polynomial when we restrict to matroids. The second section is concerned with split matroids, a class of matroids which arises by putting conditions on the system of split hyperplanes of the matroid base polytope. We describe these conditions in terms of structural properties of the matroid, and use this to give an excluded minor characterisation of the class. In the nal section, we investigate the structure of clutters. A clutter consists of a nite set and a collection of pairwise incomparable subsets. Clutters are natural generalisations of matroids, and they have similar operations of deletion and contraction. We introduce a notion of connectivity for clutters that generalises that of connectivity for matroids. We prove a splitter theorem for connected clutters that has the splitter theorem for connected matroids as a special case: if M and N are connected clutters, and N is a proper minor of M, then there is an element in E(M) that can be deleted or contracted to produce a connected clutter with N as a minor