The Public Education Tax Credit

Public education is an end, not a means. For a democratic nation to thrive, its schools must prepare children not only for success in private life but for participation in public life. It must foster harmonious social relations among the disparate groups in our pluralistic society and ensure universal access to a quality education. Unfortunately, the American school system has long fallen short as a means of fulfilling these purposes. This paper offers a more effective way of delivering on the promise of public education, by ensuring that all families have the means to choose their children's schools from a diverse market of education providers. All education providers -- government, religious, and secular -- can contribute to public education because all can serve the public by educating children. Educational freedom can most effectively be realized through nonrefundable education tax credits -- for both parents' education costs for their own children and taxpayer donations to nonprofit scholarship funds. This paper argues that tax credits enjoy practical, legal, and political advantages over school vouchers. These advantages are even more important for choice programs that target low-income children, as tax credits mitigate some disadvantages inherent to targeted programs. It also contends that broad-based programs are superior to narrowly targeted ones, even when the goal is specifically to serve disadvantaged students. Targeted programs are fundamentally inferior -- in both practical and strategic terms -- to broad-based programs that include the voting middle class. Finally, accountability in education means accountability to parents and taxpayers. Education tax credits afford this accountability without the need for intrusive government regulations that create political and market liabilities for school choice policies. To date, school choice policy has spread and grown only slowly, in part because of inadequate legislation. Existing school choice laws fall short in terms of both market principles and political considerations. Pursuing a policy that follows more closely what works economically and politically should increase the likelihood of long-term legislative success, program success, program survival, and program expansion

Regular colored graphs of positive degree

Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of regular colored graphs of fixed positive degree and perform their exact and asymptotic enumeration. In particular we show that the generating function of the family of graphs of fixed degree is an algebraic series with a positive radius of convergence, independant of the degree. We describe the singular behavior of this series near its dominant singularity, and use the results to establish the double scaling limit of colored tensor models.Comment: Final version. Significant improvements made, main results unchange

Closed, Palindromic, Rich, Privileged, Trapezoidal, and Balanced Words in Automatic Sequences

We prove that the property of being closed (resp., palindromic, rich, privileged trapezoidal, balanced) is expressible in first-order logic for automatic (and some related) sequences. It therefore follows that the characteristic function of those n for which an automatic sequence x has a closed (resp., palindromic, privileged, rich, trape- zoidal, balanced) factor of length n is automatic. For privileged words this requires a new characterization of the privileged property. We compute the corresponding characteristic functions for various famous sequences, such as the Thue-Morse sequence, the Rudin-Shapiro sequence, the ordinary paperfolding sequence, the period-doubling sequence, and the Fibonacci sequence. Finally, we also show that the function counting the total number of palindromic factors in a prefix of length n of a k-automatic sequence is not k-synchronized

A combinatorial approach to jumping particles

In this paper we consider a model of particles jumping on a row of cells, called in physics the one dimensional totally asymmetric exclusion process (TASEP). More precisely we deal with the TASEP with open or periodic boundary conditions and with two or three types of particles. From the point of view of combinatorics a remarkable feature of this Markov chain is that it involves Catalan numbers in several entries of its stationary distribution. We give a combinatorial interpretation and a simple proof of these observations. In doing this we reveal a second row of cells, which is used by particles to travel backward. As a byproduct we also obtain an interpretation of the occurrence of the Brownian excursion in the description of the density of particles on a long row of cells.Comment: 24 figure

Quantum fields on curved spacetimes and a new look at the Unruh effect

We describe a new viewpoint on canonical quantization of linear fields on a general curved background that encompasses and generalizes the standard treatment of canonical QFT given in textbooks. Our method permits the construction of pure states and mixed stated with the same technique. We apply our scheme to the study of Rindler QFT and we present a new derivation of the Unruh effect based on invariance arguments