Multiple partitions, lattice paths and a Burge-Bressoud-type correspondence

A bijection is presented between (1): partitions with conditions $f_j+f_{j+1}\leq k-1$ and $f_1\leq i-1$, where $f_j$ is the frequency of the part $j$ in the partition, and (2): sets of $k-1$ ordered partitions $(n^{(1)}, n^{(2)}, ..., n^{(k-1)})$ such that $n^{(j)}_\ell \geq n^{(j)}_{\ell+1} + 2j$ and $n^{(j)}_{m_j} \geq j+ {\rm max} (j-i+1,0)+ 2j (m_{j+1}+... + m_{k-1})$, where $m_j$ is the number of parts in $n^{(j)}$. This bijection entails an elementary and constructive proof of the Andrews multiple-sum enumerating partitions with frequency conditions. A very natural relation between the $k-1$ ordered partitions and restricted paths is also presented, which reveals our bijection to be a modification of Bressoud's version of the Burge correspondence.Comment: 12 pages; minor corrections, version to appear in Discrete Mat

Local Technological and Demographic Effects on Electricity Transmission: A Spatially Lagged Local Estimation of New England Marginal Losses

Electricity transmission is subject to distribution losses and congestion costs. Economists have prior theorized that these transmission imperfections could create divided markets with electricity generating spatial oligopolists. This concern has been largely dismissed because of recent technological advances in electricity transmission. The effects of local technological and demographic indicators on electricity transmission costs remains both commonly accepted as negligible and spatially untested. This analysis employs a spatially lagged local estimation of New England’s marginal electricity losses with respect to both technological and demographic indicators. The results of this analysis are consistent with the widely accepted notion that technological advances have mitigated the effect of local distribution losses and local congestion costs on electricity prices

Accurate Economics to Protect Endangered Species and their Critical Habitats

Federal agencies currently use a methodology that finds negligible benefits of protecting critical habitat for endangered species, despite the prime real estate that is often involved. The Endangered Species Act already calls for economic analysis, but agencies currently treat it as a meaningless hoop to jump through. Agencies justify this hollow exercise by pointing to the difficulty in quantifying the increment of added protection that comes with critical habitat designation. However, the increment of added protection for critical habitat can be measured using methods already employed by agencies in other environmental analyses. Although the central benefits of critical habitat are improvements to the condition of listed species, accurate economic analysis should also consider the broad benefits of ecosystem services that flow from protected areas to human populations. I propose that agencies use a methodology that weighs the estimated burdens on regulated parties against the estimated benefits of designating lands as critical habitat. My proposed—more accurate—analysis can lead to more effective implementation of the Endangered Species Act by allowing agencies to target limited resources to projects that offer high net conservation benefits. I use a recent cost-benefit analysis for loggerhead turtles to demonstrate that the benefits of conserving habitat include increased protection of the species as well as a larger flow of ecosystem services amounting to at least $106 million per year in benefits, not the$0 estimate that federal agencies have arrived at. Accurate economic analysis provides useful information to agencies and the public in a way that can improve discussions that are often one-sided because of an emphasis on regulatory costs with little discussion of regulatory benefits

Embedding of bases: from the M(2,2k+1) to the M(3,4k+2-delta) models

A new quasi-particle basis of states is presented for all the irreducible modules of the M(3,p) models. It is formulated in terms of a combination of Virasoro modes and the modes of the field phi_{2,1}. This leads to a fermionic expression for particular combinations of irreducible M(3,p) characters, which turns out to be identical with the previously known formula. Quite remarkably, this new quasi-particle basis embodies a sort of embedding, at the level of bases, of the minimal models M(2,2k+1) into the M(3,4k+2-delta) ones, with 0 \leq delta \leq 3.Comment: corrected a typo in the title, 7 page

Fermionic characters for graded parafermions

Fermionic-type character formulae are presented for charged irreduciblemodules of the graded parafermionic conformal field theory associated to the coset $osp(1,2)_k/u(1)$. This is obtained by counting the weakly ordered `partitions' subject to the graded $Z_k$ exclusion principle. The bosonic form of the characters is also presented.Comment: 24 p. This corrects typos (present even in the published version) in eqs (4.4), (5.23), (5.24) and (C.4

Maintaining an ethical balance in the curriculum design of games-based degrees.

In February 2011, games-based degrees were subjected to the scrutiny of the Livingstone- Hope report into the future of education in the fields of video games and visual effects. The report delivers a damning appraisal of the education system’s ability to fulfil skills shortages in these creative industries, and makes a range of proposals for changing education in both schools and universities to meet the needs of these sectors. This paper discusses the findings of this report from the perspective of higher education, with particular emphasis on the complex ethical considerations of designing a curriculum for games-based degrees. The argument for taking a broader perspective on this issue is illustrated through discussion of Games Software Development degrees at Sheffield Hallam University

A Combinatorial Model for Exceptional Sequences in Type A

Exceptional sequences are certain ordered sequences of quiver representations. We use noncrossing edge-labeled trees in a disk with boundary vertices (expanding on T. Araya's work) to classify exceptional sequences of representations of Q, the linearly-ordered quiver with n vertices. We also show how to use variations of this model to classify c-matrices of Q, to interpret exceptional sequences as linear extensions, and to give a simple bijection between exceptional sequences and certain chains in the lattice of noncrossing partitions. In the case of c-matrices, we also give an interpretation of c-matrix mutation in terms of our noncrossing trees with directed edges.Comment: 18 page