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Open Access research with a European policy impact...

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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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An involution on bicubic maps and β(0, 1)-trees

Claesson, Anders and Kitaev, Sergey and de Mier, Anna (2015) An involution on bicubic maps and β(0, 1)-trees. Australasian Journal of Combinatorics, 61 (1). pp. 1-18. ISSN 1034-4942

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Bicubic maps are in bijection with β(0, 1)-trees. We introduce two new ways of decomposing β(0, 1)-trees. Using this we dene an endofunction on β(0, 1)-trees, and thus also on bicubic maps. We show that this endofunction is in fact an involution. As a consequence we are able to prove some surprising results regarding the joint equidistribution of certain pairs of statistics on trees and maps. Finally, we conjecture the number of fixed points of the involution.