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On the Diameter of the Rotation Graph of Binary Coupling Trees
, 1999
"... A binary coupling tree on n+1 leaves is a 02tree in which each leaf has a distinct label. The rotation graph Gn is defined as the graph of all binary coupling trees on n + 1 leaves, with edges connecting trees that can be transformed into each other by a single rotation. In this paper we study d ..."
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Mathematics and Computer Science, University of Ghent, Krijgslaan 281S9, B9000 Gent, Belgium. Tel. ++ 32 9 2644808; Fax ++ 32 9 2644995; Email Veerle.Fack@rug.ac.be. 1 Research Associate of the Fund for Scientific Research  Flanders (Belgium) 1 Introduction Binary coupling trees arise in the context
Construction techniques for incidence structures
 In Combinatorics 2004 conference (Sicilie
"... A balanced incomplete block design (BIBD) [1] is a pair (V,B) where V is a vset and B is a collection of b ksubsets of V (blocks) such that each element of V is contained in exactly r blocks and any 2subset of V is contained in exactly λ blocks. The partial geometry with parameters PG(s, t, α) is ..."
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A balanced incomplete block design (BIBD) [1] is a pair (V,B) where V is a vset and B is a collection of b ksubsets of V (blocks) such that each element of V is contained in exactly r blocks and any 2subset of V is contained in exactly λ blocks. The partial geometry with parameters PG(s, t, α) is defined as a set S = (P,B, I) with points P and lines B disjoint (nonempty) sets of objects, and I is a symmetric pointline incidence relation I ⊆ (P ×B) ∪ (B × P). Each point (line) is incident with 1 + t (1 + s) lines and two different points (lines) are incident with at most one line (point). If x is a point not incident with line L, then exactly α (α ≥ 1) points y1, y2,..., yα and α lines M1,M2,...,Mα exist such that xIMi, MiIyi, yiIL (∀i: 1 ≤ i ≤ α) We combine a standard orderly algorithm with techniques from the field of Constraint Satisfaction Problems (CSP). We present some results, for instance we found that there is no PG(6, 6, 4) when assuming an automorphism of order 3 with 7 fixed points and 7 fixed blocks. When assuming a fixed automorphism, an orbit matrix generation phase which precedes the
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"... Competitive graph searches. (English summary) ..."
Hadamard matrices of order 36 and doubleeven selfdual [72, 36, 12] codes
 European Conference on Combinatorics, Graph Theory and Applications 2005, volume AE of DMTCS Proceedings, pages 93–98. Discrete Mathematics and Theoretical Computer Science
, 2005
"... (35, 17, 8) designs with an automorphism of order 3 and 2 fixed points and blocks. ..."
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(35, 17, 8) designs with an automorphism of order 3 and 2 fixed points and blocks.
On minimal blocking sets of the generalized quadrangle Q(4, q)
"... The generalized quadrangle Q(4, q) arising from the parabolic quadric in P G(4, q) always has an ovoid. It is not known whether a minimal blocking set of size smaller than q 2 + q (which is not an ovoid) exists in Q(4, q), q odd. We present results on smallest blocking sets in Q(4, q), q odd, obtain ..."
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The generalized quadrangle Q(4, q) arising from the parabolic quadric in P G(4, q) always has an ovoid. It is not known whether a minimal blocking set of size smaller than q 2 + q (which is not an ovoid) exists in Q(4, q), q odd. We present results on smallest blocking sets in Q(4, q), q odd, obtained by a computer search. For q = 5, 7, 9, 11 we found minimal blocking sets of size q 2 + q − 2 and we discuss their structure. By an exhaustive search we excluded the existence of a minimal blocking set of size q 2 + 3 in Q(4, 7).
GrInvIn for Graph Theory Teaching and Research
, 2007
"... Various programs to support research in graph theory have been developed and successfully used, such as AGX/AGX2[1], Cabrigraph[2], Graffiti[3], Graffiti.pc[4], GRAPH[5], GraPHedron[6], LINK[7], and newGRAPH[8]. Some of them emphasize the manipulation of graphs and computation of invariants, other ..."
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Various programs to support research in graph theory have been developed and successfully used, such as AGX/AGX2[1], Cabrigraph[2], Graffiti[3], Graffiti.pc[4], GRAPH[5], GraPHedron[6], LINK[7], and newGRAPH[8]. Some of them emphasize the manipulation of graphs and computation of invariants, others focus on (graph) conjecturing. As to the goal of GrInvIn we were most influenced by Graffiti.pc which was developed by Ermelinda DeLaVina. It was created for research in graph theory as well as for teaching graph theory by means of graph conjecturing. The GrInvIn framework provides the core functionality needed to implement an application for graph theory in general. It includes basic functionality to work with graphs, invariants, and conjectures. In addition to data structures and interfaces for these concepts, the framework also provides a basic graph editor, various invariant computing routines, and an intuitive graphical user interface. GrInvIn is still being developed and soon further functionality (such as graph generation programs) will be added. In order to guarantee portability, the interface and most of the subroutines are written in the highly portable programming language Java. Some parts that are performance critical and interact less with the operating system are written in C.
On the enumeration of uniquely reducible double designs
"... A double 2(v,k,2λ) design is a design which is reducible into two 2(v,k,λ) designs. It is called uniquely reducible if it has, up to equivalence, only one reduction. We present properties of uniquely reducible double designs which show that their total number can be determined if only the designs ..."
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A double 2(v,k,2λ) design is a design which is reducible into two 2(v,k,λ) designs. It is called uniquely reducible if it has, up to equivalence, only one reduction. We present properties of uniquely reducible double designs which show that their total number can be determined if only the designs with nontrivial automorphisms are classified with respect to their automorphism group. As an application, after proving that a reducible 2(21,5,2) design is uniquely reducible, we establish that the number of all reducible 2(21,5,2) designs is 1 746 461 307.
ANALYSING EYE MOVEMENT PATTERNS TO IMPROVE MAP DESIGN
"... Recently, the use of eye tracking systems has been introduced in the field of cartography and GIS to support the evaluation of the quality of maps towards the user. The quantitative eye movement metrics are related to for example the duration or the number of the fixations which are subsequently (st ..."
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Recently, the use of eye tracking systems has been introduced in the field of cartography and GIS to support the evaluation of the quality of maps towards the user. The quantitative eye movement metrics are related to for example the duration or the number of the fixations which are subsequently (statistically) compared to detect significant differences in map designs or between different user groups. Hence, besides these standard eye movement metrics, other more spatial measurements and visual interpretations of the data are more suitable to investigate how users process, store and retrieve information from a (dynamic and/or) interactive map. This information is crucial to get insights in how users construct their cognitive map: e.g. is there a general search pattern on a map and which elements influence this search pattern, how do users orient a map, what is the influence of for example a pan operation. These insights are in turn crucial to be able to construct more effective maps towards the user, since the visualisation of the information on the map can be keyed to the user his cognitive processes. The study focuses on a qualitative and visual approach of the eye movement data resulting from a user study in which 14 participants were tested while working on 20 different dynamic and interactive demomaps. Since maps are essentially spatial objects, the analysis of these eye movement data is directed towards the locations of the fixations, the visual representation of the scanpaths, clustering and aggregation of the scanpaths. The results from this study show interesting patterns in the search strategies of users on dynamic and interactive maps.
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