Maximal partial spreads and the modular n-queen problem III

AbstractMaximal partial spreads in PG(3,q)q=pk,p odd prime and q⩾7, are constructed for any integer n in the interval (q2+1)/2+6⩽n⩽(5q2+4q−1)/8 in the case q+1≡0,±2,±4,±6,±10,12(mod24). In all these cases, maximal partial spreads of the size (q2+1)/2+n have also been constructed for some small values of the integer n. These values depend on q and are mainly n=3 and n=4. Combining these results with previous results of the author and with that of others we can conclude that there exist maximal partial spreads in PG(3,q),q=pk where p is an odd prime and q⩾7, of size n for any integer n in the interval (q2+1)/2+6⩽n⩽q2−q+2

Partial ovoids and partial spreads in finite classical polar spaces

We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces

Maximal partial line spreads of non-singular quadrics

For n >= 9 , we construct maximal partial line spreads for non-singular quadrics of for every size between approximately and , for some small constants and . These results are similar to spectrum results on maximal partial line spreads in finite projective spaces by Heden, and by Gacs and SzAnyi. These results also extend spectrum results on maximal partial line spreads in the finite generalized quadrangles and by Pepe, Roing and Storme

Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces

2000 Mathematics Subject Classification: 05B25, 51E20.We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces.The research of the fourth author was also supported by the Project Combined algorithmic and the oretical study of combinatorial structur es between the Fund for Scientific Research Flanders-Belgium (FWO-Flanders) and the Bulgarian Academy of Science

Constant rank-distance sets of hermitian matrices and partial spreads in hermitian polar spaces

In this paper we investigate partial spreads of $H(2n-1,q^2)$ through the related notion of partial spread sets of hermitian matrices, and the more general notion of constant rank-distance sets. We prove a tight upper bound on the maximum size of a linear constant rank-distance set of hermitian matrices over finite fields, and as a consequence prove the maximality of extensions of symplectic semifield spreads as partial spreads of $H(2n-1,q^2)$. We prove upper bounds for constant rank-distance sets for even rank, construct large examples of these, and construct maximal partial spreads of $H(3,q^2)$ for a range of sizes

The geproci property in positive characteristic

The geproci property is a recent development in the world of geometry. We call a set of points $Z\subseteq\mathbb{P}_k^3$ an $(a,b)$-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point $P$ to a plane is a complete intersection of curves of degrees $a\leq b$. Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were found starting in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids. Before the work in this paper -- based partly on the author's thesis -- only a few examples of geproci nontrivial non-grid non-half grids were known and there was no known way to generate more. Here, we use geometry in the positive characteristic setting to give new methods of producing geproci half grids and non-half grids.Comment: 16 pages, 2 figure

A fuzzy taxonomy for e-Health projects

Evaluating the impact of Information Technology (IT) projects represents a problematic task for policy and decision makers aiming to define roadmaps based on previous experiences. Especially in the healthcare sector IT can support a wide range of processes and it is difficult to analyze in a comparative way the benefits and results of e-Health practices in order to define strategies and to assign priorities to potential investments. A first step towards the definition of an evaluation framework to compare e-Health initiatives consists in the definition of clusters of homogeneous projects that can be further analyzed through multiple case studies. However imprecision and subjectivity affect the classification of e-Health projects that are focused on multiple aspects of the complex healthcare system scenario. In this paper we apply a method, based on advanced cluster techniques and fuzzy theories, for validating a project taxonomy in the e-Health sector. An empirical test of the method has been performed over a set of European good practices in order to define a taxonomy for classifying e-Health projects.Evaluating the impact of Information Technology (IT) projects represents a problematic task for policy and decision makers aiming to define roadmaps based on previous experiences. Especially in the healthcare sector IT can support a wide range of processes and it is difficult to analyze in a comparative way the benefits and results of e-Health practices in order to define strategies and to assign priorities to potential investments. A first step towards the definition of an evaluation framework to compare e-Health initiatives consists in the definition of clusters of homogeneous projects that can be further analyzed through multiple case studies. However imprecision and subjectivity affect the classification of e-Health projects that are focused on multiple aspects of the complex healthcare system scenario. In this paper we apply a method, based on advanced cluster techniques and fuzzy theories, for validating a project taxonomy in the e-Health sector. An empirical test of the method has been performed over a set of European good practices in order to define a taxonomy for classifying e-Health projects.Articles published in or submitted to a Journal without IF refereed / of international relevanc