Multihomogeneous resultant formulae by means of complexes

We provide conditions and algorithmic tools so as to classify and construct the smallest possible determinantal formulae for multihomogeneous resultants arising from Weyman complexes associated to line bundles in products of projective spaces. We also examine the smallest Sylvester-type matrices, generically of full rank, which yield a multiple of the resultant. We characterize the systems that admit a purely B\'ezout-type matrix and show a bijection of such matrices with the permutations of the variable groups. We conclude with examples showing the hybrid matrices that may be encountered, and illustrations of our Maple implementation. Our approach makes heavy use of the combinatorics of multihomogeneous systems, inspired by and generalizing results by Sturmfels-Zelevinsky, and Weyman-Zelevinsky.Comment: 30 pages. To appear: Journal of Symbolic Computatio

Exact resultants for corner-cut unmixed multivariate polynomial systems using the dixon formulation

Structural conditions on the support of a multivariate polynomial system are developed for which the Dixon-based resultant methods compute exact resultants. For cases when this cannot be done, an upper bound on the degree of the extraneous factor in the projection operator can be determined a priori, thus resulting in quick identification of the extraneous factor in the projection operator. (For the bivariate case, the degree of the extraneous factor in a projection operator can be determined a priori.) The concepts of a corner-cut support and almost corner-cut support of an unmixed polynomial system are introduced. For generic unmixed polynomial systems with corner-cut and almost corner-cut supports, the Dixon based methods can be used to compute their resultants exactly. These structural conditions on supports are based on analyzing how such supports differ from box supports of n-degree systems for which the Dixon formulation is known to compute the resultants exactly. Such an analysis also gives a sharper bound on the complexity of resultant computation using the Dixon formulation in terms of the support and the mixed volume of the Newton polytope of the support. These results are a direct generalization of the authors ’ results on bivariate systems including the results of Zhang and Goldman as well as of Chionh for generic unmixed bivariate polynomial systems with corner-cut supports

‘Super disabilities’ vs ‘Disabilities’?:Theorizing the role of ableism in (mis)representational mythology of disability in the marketplace

People with disabilities (PWD) constitute one of the largest minority groups with one in five people worldwide having a disability. While recognition and inclusion of this group in the marketplace has seen improvement, the effects of (mis)representation of PWD in shaping the discourse on fostering marketplace inclusion of socially marginalized consumers remain little understood. Although effects of misrepresentation (e.g., idealized, exoticized or selective representation) on inclusion/exclusion perceptions and cognitions has received attention in the context of ethnic/racial groups, the world of disability has been largely neglected. By extending the theory of ableism into the context of PWD representation and applying it to the analysis of the We’re the Superhumans advertisement developed for the Rio 2016 Paralympic Games, this paper examines the relationship between the (mis)representation and the inclusion/exclusion discourse. By uncovering that PWD misrepresentations can partially mask and/or redress the root causes of exclusion experienced by PWD in their lived realities, it contributes to the research agenda on the transformative role of consumption cultures perpetuating harmful, exclusionary social perceptions of marginalized groups versus contributing to advancement of their inclusion