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                <text>A Bedfordshire Vicar and his Drinking Companions: &#13;
The Case of John Bolton (1716)</text>
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              <text>For an oriented graph D, the inversion of X ⊆ V(D) in D is the graph obtained by reversing the orientation of all arcs with both ends in X. The inversion number inv(D) is the minimum number of inversions needed to obtain an acyclic oriented graph. We show that the dijoin conjecture of Bang-Jensen, da Silva and Havet, that inv( D 1 → D 2) = inv( D 1) + inv( D 2), is true in the case where inv( D 1) = 2 and inv( D 2) is even. We also characterise the cases inv( D 1) = 2 and inv( D 2) odd, for which the conjecture does and does not hold. We then go on to show a similar result for n-joins, in doing so we prove a conjecture of Alon, Powierski, Savery, Scott and Wilmer. Our proofs build on the idea of tournament minimum rank, introduced by Behague, Johnston, Morrison and Ogden.</text>
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                <text>Natalie Behague</text>
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                <text>A case of the dijoin conjecture on inverting oriented graphs</text>
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              <text>Housing affordability is a key issue in British politics and around  the world. One policy approach to address this problem is to expand the supply of housing through new development. However, new development can often generate controversy among existing residents. This research aims to better understand resident objections against new development. A methodology was developed to collect objections from publicly available planning applications.  In total, 1975 objections across 82 major housing planning applications were collected, all in the Bradford region. The objections were categorised into 31 issues  and subsequently analysed for patterns and themes using statistical techniques. There were three key findings: first, that environmental issues are most important for residents; second, a small number of applications cause the majority of objections; third, the affluence of a wards impacts engagement in the planning process.</text>
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                <text>A Case Study in Planning and Housing: Examining objections to housing development in Bradford</text>
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                <text>Mareike Beck &amp;  Blake Jeffcott</text>
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