Frank Scott Musical Arrangements, 1970s-1990s

Collection of 273 music arrangements by Frank Scott for use by his orchestra in California until his death

Crystallographic arrangements: Weyl groupoids and simplicial arrangements

We introduce the simple notion of a "crystallographic arrangement" and prove a one-to-one correspondence between these arrangements and the connected simply connected Cartan schemes for which the real roots are a finite root system (up to equivalence on both sides). We thus obtain a more accessible definition for this very large subclass of the class of simplicial arrangements for which a complete classification is known.Comment: 13 page

Estimating the efficiency gains of debt restructuring

One rationale for debt reduction operations under the Brady Plan has been, by alleviating the debt overhang, to improve investment efficiency. Brady-type debt and debt-service reduction (within a strong policy framework, where there is a track record of economic adjustment) has been shown to affect development significantly. The principle benefit of eliminating the debt overhang is to improve investment incentives for private investors - direct liquidity relief is secondary. So, evaluating a debt and debt-service reduction operation should involve estimating efficiency gains as well as direct financial savings. The authors present a method (requiring only weak assumptions) for establishing an upper bound on the efficiency impact of debt reductions. The key reference framework for evaluating much more complex Brady-type debt deals is open-market buybacks. Their approach to determining this upper bound hinges on the assumption that efficiency gains on a straight open-market repurchase of debt never exceed the gains to creditors. If an open-market buyback indeed reduces the debt overhang and moves a country toward more (and more efficient) investment, creditors will anticipate this in setting a price for remitting their claims. So, at least part of the efficiency gains are dissipated in additional capital gains to creditors. To give point estimates to efficiency gains, they develop a simple two-period model of debt overhang and investment and discuss assumptions under which it is possible to obtain a closed-form solution to the model. Their empirical estimates indicate that the general bounds derived in the first step tend to overstate substantially the efficiency gains of debt reduction operations. In Mexico's case, for example, the upper-bound estimate of efficiency gains is US $15 billion, but the point estimate is only about US$1 billion. What are the policy implications of their low point estimates? The debt-overhang disincentive may not be as important as the broader problem of debtors'credit constraints in international capital markets. How can new loan packages to developing countries be structured to maximize investment incentives? By using loans rather than outright grants, donors can give a country more funds for current investment at lower present dicounted expense. But grants, unlike loans, do not distort investment incentives. In short, if a credit-constrained country starts with no debt overhang, the first tranche of aid should probably be in hard loans. As total transfers increase, if the borrowing country has not gained access to private capital markets, marginal transfers should be grants. The optimal strategy for new flows can involve both increasing grants and decreasing loans. When transfers are expected to be heavy, a case can be made for using grants exclusively.Strategic Debt Management,Economic Theory&Research,Financial Crisis Management&Restructuring,Banks&Banking Reform,Environmental Economics&Policies

Bigraphical Arrangements

We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson. A consequence is a new proof of a bijection between labeled graphs and regions of the Shi arrangement first given by Stanley. We also give bounds on the number of regions of a bigraphical arrangement.Comment: Added Remark 19 addressing arbitrary G-parking functions; minor revision

Freeness of Hyperplane Arrangements between Boolean Arrangements and Weyl Arrangements of Type Bℓ B_{\ell}

Every subarrangement of Weyl arrangements of type $B_{\ell}$ is represented by a signed graph. Edelman and Reiner characterized freeness of subarrangements between type $A_{\ell-1}$ and type $B_{\ell}$ in terms of graphs. Recently, Suyama and the authors characterized freeness for subarrangements containing Boolean arrangements satisfying a certain condition. This article is a sequel to the previous work. Namely, we give a complete characterization for freeness of arrangements between Boolean arrangements and Weyl arrangements of type $B_{\ell}$ in terms of graphs.Comment: 15 page