Proofs of some binomial identities using the method of last squares

We give combinatorial proofs for some identities involving binomial sums that have no closed form.Comment: 8 pages, 16 figure

Sandpiles and Dominos

We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular checkerboard; (ii) a product of special values of Chebyshev polynomials; and (iii) a double-product whose factors are sums of squares of values of trigonometric functions. We provide a new derivation of the formula due to Kasteleyn and to Temperley and Fisher for counting the number of domino tilings of a 2m x 2n rectangular checkerboard and a new way of counting the number of domino tilings of a 2m x 2n checkerboard on a M\"obius strip.Comment: 35 pages, 24 figure

Managing the Noodle Bowl: The Fragility of East Asian Regionalism

The paper argues that East Asian regionalism is fragile because (i) each nation's industrial competitiveness depends on the smooth functioning of "Factory Asia" - in particular for intraregional trade; (ii) the unilateral tariff-cutting that created Factory Asia is not subject to WTO discipline (bindings); (iii) there is no "top-level management"; to substitute for WTO discipline, to ensure that bilateral trade tensions - tensions that are inevitable in East Asia - do not spill over into region-wide problems due to lack of cooperation and communication. This paper argues that the window of opportunity for East Asian vision was missed; what East Asia needs now is management, not vision. East Asia should launch a "New East Asian Regional Management Effort" with a reinforced ASEAN+3 leading the way. The first priority should be to bind the region's unilateral tariff cuts into the WTO.Asian integration; free trade agreement; best practices; Asian development

Multilateralising Regionalism: Spaghetti Bowls as Building Blocs on the Path to Global Free Trade

This paper addresses the final steps to global free trade -- the political economy forces that might drive them, and the role the WTO might play in guiding them. Two facts form the departure point: 1) Regionalism is here to stay; 2) the motley assortment of regional trade agreements is not the best way to organise world trade. Moving to global duty-free trade will require a multilateralisation of regionalism. The paper presents the political economy logic of trade liberalisation and uses it to structure a narrative of world trade liberalisation since 1947. The logic is then used to project the world tariff map in 2010, arguing that the pattern will be marked by fractals – fuzzy, leaky trade blocs made up of fuzzy, leaky sub-blocs (fuzzy since the proliferation of FTAs makes it impossible to draw sharp lines around the 3 big blocs, and leaky since some FTAs create free trade ’canals’ linking the blocs). The paper then presents a novel political economy mechanism – spaghetti bowls as building blocs – whereby offshoring creates a force that encourages the multilateralisation of regionalism. Finally, the paper suggests three things the WTO could do to help multilateralise regionalism.

Bijections for Entringer families

Andr\'e proved that the number of alternating permutations on $\{1, 2, \dots, n\}$ is equal to the Euler number $E_n$. A refinement of Andr\'e's result was given by Entringer, who proved that counting alternating permutations according to the first element gives rise to Seidel's triangle $(E_{n,k})$ for computing the Euler numbers. In a series of papers, using generating function method and induction, Poupard gave several further combinatorial interpretations for $E_{n,k}$ both in alternating permutations and increasing trees. Kuznetsov, Pak, and Postnikov have given more combinatorial interpretations of $E_{n,k}$ in the model of trees. The aim of this paper is to provide bijections between the different models for $E_{n,k}$ as well as some new interpretations. In particular, we give the first explicit one-to-one correspondence between Entringer's alternating permutation model and Poupard's increasing tree model.Comment: 19 page