13 research outputs found
Bounds on the diameter of Cayley graphs of the symmetric group
In this paper we are concerned with the conjecture that, for any set of
generators S of the symmetric group of degree n, the word length in terms of S
of every permutation is bounded above by a polynomial of n. We prove this
conjecture for sets of generators containing a permutation fixing at least 37%
of the points.Comment: 17 pages, 6 table
Expansion in perfect groups
Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an
integer q, denote by Ga_q the subgroup of Ga consisting of the elements that
project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q
with respect to the generating set S form a family of expanders when q ranges
over square-free integers with large prime divisors if and only if the
connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas
are explained in more details in the introduction, typos corrected, results
and proofs unchange
Expansion in SL_d(Z/qZ), q arbitrary
Let S be a fixed finite symmetric subset of SL_d(Z), and assume that it
generates a Zariski-dense subgroup G. We show that the Cayley graphs of pi_q(G)
with respect to the generating set pi_q(S) form a family of expanders, where
pi_q is the projection map Z->Z/qZ
Some Additive Combinatorics Problems in Matrix Rings
We study the distribution of singular and unimodular matrices in sumsets in
matrix rings over finite fields. We apply these results to estimate the largest
prime divisor of the determinants in sumsets in matrix rings over the integers
The future of food security, environments and livelihoods in Western Africa. Four socio-economic scenarios. CCAFS Working Paper no. 130.
This working paper examines the development of regional socioeconomic scenarios for West Africaâs development, agriculture, food security and climate impacts. We present four globally consistent regional scenarios framed and outlined by regional experts who crafted narratives and determined key drivers of change. Stakeholders identified the type of actors driving change and the timeline of strategic planning as the most uncertain and most relevant
factors of change affecting food security, livelihoods and environments in the region.
The scenarios were linked to the IPCC communityâs global Shared Socio-economic Pathways(SSPs) and quantified using two agricultural economic models, GLOBIOM and IMPACT, in interaction with drivers outlined by the SSPs and guided by semi-quantitative information from the stakeholders. The quantification of the scenarios has provided additional insights into the possible development of Western Africa in the context of a global economy as well as how the agricultural sector may be affected by climate change. The scenarios process highlights the need to combine socio-economic and climate scenarios, to base these scenarios in regional expertise, and ways to make scenarios useful for policy design.
The objective of this working paper is to provide scenarios for future regional development for West Africa on the future of food security, environment, and rural livelihoods as well as offer details of the multi-stakeholder scenarios development process. Using both qualitative and quantitative scenarios we provide insights into the possible development of West Africa as well as a scalable framework for regional decision makers and the scientific community to use scenarios to build and test policies to make them more robust in the face of future uncertainty.
In these scenarios, strong economic development increases food security and agricultural development. Increased crop and livestock productivity may lead to an expansion of agricultural areas within the region but productivity improvements may reduce the pressure on land elsewhere. In the context of a global economy, West Africa remains a large consumer and producer of a selection of commodities. However, the growth in population in combination with rising incomes may lead to increases in the regionâs imports. For West Africa, climate change is likely to have negative effects on both crop yields and grassland productivity, and lack of investment in agriculture may exacerbate them.
The aim of the regional scenarios is provide challenging contexts for policy makers to test and develop a range of national and regional policies. To date, the scenarios have been used in a number of policy design processes which include collaborations with ECOWAS priority setting, the National Plan for the Rural Sector for Burkina Faso (PNSR), and district and national level policy processes in Ghana
Séminaire Bourbaki Volume 2016/2017 Exposés 1120-1135
International audienc