1 On a Conjecture of A. Hartman. - 1 Notations and Preliminaries. - 2 The Structure of Trades. - 3 Block Size 3 and Strength 2. - 4 A Possible Approach to the Problem. - 5 The Case of Strength 2. - 6 Some Examples. - 7 Concluding Remarks. - 2 Some Problems in Total Graph Theory. - 1 Introduction and Preliminaries. - 2 Total Ramsey Numbers. - 3 Vertex Reconstructibility of Total Graphs. - 4 Edge Reconstructibility of Total Graphs. - 5 The Spectrum of Total Graphs. - 6 Groups and Polynomials of Graphs. - 7 Relationships Between some Parameters of G and those of T(G). - 8 Some Generalizations and Applications. - 9 Upper Bounds for x? (G). - 10 Remarks. - 3 Construction Techniques for Mutually Orthogonal Latin Squares. - 1 Background. - 2 History and Small Orders. - 3 Pairwise balanced designs and Greig's line-flip. - 4 Difference matrices: some direct constructions. - 5 A variant of Wilson's theorem. - 6 Concluding remarks. - 4 The Spectrum of R-Orthogonal Latin Squares. - 1 Latin squares and r-orthogonality. - 2 Some basic constructions. - 3 Small sides. - 4 A GDD construction. - 5 Intermediate sides. - 5 General Theory of Translation Invariant Systems. - 1 Introduction. - 2 The Model. - 3 A Residuated Semigroup. - 4 Some Basic Questions. - 6 Some Mathematical Problems Arising in Molecular Bioinformatics: The Concept of Bioinformatics. - 1 Introduction. - 2 The concept of sequence space. - 3 The geometry of sequence space. - 4 Cluster analysis. - 5 Split decomposition. - 6 Concluding remark. - 7 An Algorithmic Approach to Tilings. - 8 A New Connection Between Convex Geometry and Threshold Logic. - 1 Introduction. - 2 Algorithmic Enumeration of Nonisomorphic Cut-Complexes and a Generation of Convex Polytopes. - 3 Geometric Properties. - 9 The Unity of Combinatorics. - 1 Introduction. - 2 Langford's Problem. - 3Skolem's Problem. - 4 Beatty Sequences. - 5 Penrose Pieces. - 6 Wythoff's Game. - 7 Triples satisfying x + y = z. - 8 Triples satisfying x + y = 2z. - 9 Coil diagrams. - 10 Squaring the square. - 11 Packing or covering the complete graph. - 12 Hanani's cyclic Steiner systems. - 13 Perfect difference sets. - 14 Projective planes. - 15 Affine geometries. - 16 Magic squares. - 17 Kirkman's schoolgirls problem. - 18 Heawood's map on the torus. - 19 The toroidal thickness of the complete graph. - 20 Nim addition. - 21 Incidence matrices. - 22 Zarankiewicz's problem. - 23 Error-correcting codes. - 24 Hadamard matrices. - 25 Cyclic Hadamard matrices. - 26 Factoring with quadratic forms. - 27 Projective geometries. - 28 Sphere packing. - 29 Mock Turtles. - 10 Unsolved Problems in Combinatorial Games. - 11 (F 2)Rotational Steiner Triple Systems. - 1 Introduction. - 2 Skolem Sequences. - 3 Constructions. - 4 Main Results. - 12 A Simple Polynomial Time Algorithm for a Convex Hull Problem Equivalent to Linear Programming. - 1 Introduction. - 2 The Algorithm. - 13 A LinearTime Algorithm for Minimum Cost Flow on Undirected OneTrees. - 1 Introduction. - 2 The Algorithm. - 14 An Asymptotic Existence Result for Orthogonal Designs. - 1 Introduction. - 2 Basic Results. - 3 Main Results. - 15 Decomposition of Complete Tripartite Graphs Into 5-Cycles. - 1 Introduction. - 2 Necessary Conditions. - 3 An Application. - 4 Sufficiency of Conditions. - 5 Searching for a decomposition in other cases. - 16 The Nsm of a Graph. - 1 The New Stability Measure of a Graph (NSM). - 2 NSM and Operations on Graphs. - 3 Hamilton Properties of NSM. - 17 Zero-Knowledge Proofs For Independent Set and Dominating Set Problems. - 1 Introduction. - 2 A Zero-Knowledge Proof for Independent set problem. - 3 A Zero-Knowledge Proof for Dominating setproblem. - 18 Exploring the Spectrum of Values of Permanents by Simulated Annealing. - 1 The Permanent. - 2 Upper Bounds and Lower Bounds for the Permanent. - 3 Simulated Annealing. - 4 The Metropolis Algorithm. - 5 Results and Conclusions. - 19 VectorWeighted Matchings. - 1 Introduction. - 2 Preliminaries. - 3 Preference Matchings. - 4 Preference Poly topes. - 5 The Set of Efficient Solutions. - 20 Directed Quadruple Designs. - 1 Introduction. - 2 Existence of 3-(v 4 l)DDs. - 3 On the Existence of 3-(v 4 2)DDs. - 4 Some Small Cases (for ? = 2). - 21 Bounding Two-Terminal Network Reliability Via Surface Duality. - 1 Introduction. - 2 Definitions. - 3 Results. - 4 Implementation. - 5 Examples. - 22 Defining Sets for Block Designs: An Update. - 1 Introduction. - 2 Some Theoretical Results. - 3 Finding Smallest Defining Sets in Small Designs. - 4 Defining Sets in Some Infinite Classes of Designs. - 23 Open Problems at the Combinatorics Workshop of Aimc25 (Tehran 1994). Language: English