25,367 research outputs found
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
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