Women at work in Mali: the case of the Markala Cooperative

African Studies Center Working Paper No. 5

The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme

Let $Y$ denote a $D$-class symmetric association scheme with $D \geq 3$, and suppose $Y$ is almost-bipartite P- and Q-polynomial. Let $x$ denote a vertex of $Y$ and let $T=T(x)$ denote the corresponding Terwilliger algebra. We prove that any irreducible $T$-module $W$ is both thin and dual thin in the sense of Terwilliger. We produce two bases for $W$ and describe the action of $T$ on these bases. We prove that the isomorphism class of $W$ as a $T$-module is determined by two parameters, the dual endpoint and diameter of $W$. We find a recurrence which gives the multiplicities with which the irreducible $T$-modules occur in the standard module. We compute this multiplicity for those irreducible $T$-modules which have diameter at least $D-3$.Comment: 22 page

Higher Dimensional Lattice Chains and Delannoy Numbers

Fix nonnegative integers n1 , . . ., nd, and let L denote the lattice of points (a1 , . . ., ad) ∈ ℤd that satisfy 0 ≤ ai ≤ ni for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting ni = n (for all i) in these expressions yields a new proof of a recent result of Duichi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension

New proofs of the Assmus-Mattson theorem based on the Terwilliger algebra

We use the Terwilliger algebra to provide a new approach to the Assmus-Mattson theorem. This approach also includes another proof of the minimum distance bound shown by Martin as well as its dual.Comment: 15 page

Proof of the Kresch-Tamvakis Conjecture

In this paper we resolve a conjecture of Kresch and Tamvakis. Our result is the following. Theorem: For any positive integer $D$ and any integers $i,j$ $(0\leq i,j \leq D)$, the absolute value of the following hypergeometric series is at most 1: \begin{equation*} {_4F_3} \left[ \begin{array}{c} -i, \; i+1, \; -j, \; j+1 \\ 1, \; D+2, \; -D \end{array} ; 1 \right]. \end{equation*} To prove this theorem, we use the Biedenharn-Elliott identity, the theory of Leonard pairs, and the Perron-Frobenius theorem

The Multiplicities of a Dual-thin Q-polynomial Association Scheme

Let Y=(X,{Ri}1≤i≤D) denote a symmetric association scheme, and assume that Y is Q-polynomial with respect to an ordering E0,...,ED of the primitive idempotents. Bannai and Ito conjectured that the associated sequence of multiplicities mi (0≤i≤D) of Yis unimodal. Talking to Terwilliger, Stanton made the related conjecture that mi≤mi+1 and mi≤mD−i for i\u3cD/2. We prove that if Y is dual-thin in the sense of Terwilliger, then the Stanton conjecture is true

The Project‑Partnership Cycle: managing city‑university partnerships for urban sustainability and resilience transformations

Cities across the globe are striving to produce viable solutions to pressing urban sustainability and resilience problems. Despite aspirations, municipal governments often need additional support in terms of knowledge, capacity, or resources to achieve transformations. Partnerships between cities and universities are one mechanism for co-producing knowledge and achieving sustained progress on complex challenges. When properly structured and effectively managed, city-university partnerships (CUPs) are purported to increase transformative capacity in city administrations and support actions which accelerate urban transformations; but these outcomes are not always achieved. As CUPs grow in numbers, there is a pressing need to identify which principles and practices facilitate transformation. Therefore, we used iterative reflective focus group sessions to develop in-depth case studies of five sustainability and resilience CUPs across three countries. The CUPs were cross-compared to explore the partnership dynamics and management practices that aid progress towards transformative goals. Observations were then related to transformative capacity typologies, and mapped to the newly described project-partnership cycle – which is useful for the management of transformative partnerships