Combinatorial design theory is a very active area of mathematical research, with many applications in communications and information theory, computer science, statistics, engineering, and life sciences. As one of the fundamental discrete structures, combinatorial designs are used in fields as diverse as error-correcting codes, statistical design of experiments, cryptography and information secu...

In digital forensics, the issue of data integrity protection for increasingly widespread applied SSD (Solid State Disk, SSD) is to be resolved. Based on Combinatorial Group Theory, mapping data objects in SSD validation process and test object in combination group testing methods, using the non-adaptive mode to the initial calculation, stored procedures, and re-calculate, verify process, and ca...

• Encourage communication between practitioners of combinatorial and statistical design theory; make up-to-date research in combinatorics easily available to statisticians and vice versa. • Provide a standard interchange format (independent of particular software) for designs and their properties: the “External Representation”. • Provide a database of designs usable by both practising statistic...

A tutorial outline of the polyhedral theory that underlies linear programming (LP)-based combinatorial problem solving is given. Design aspects of a combinatorial problem solver are discussed in general terms. Three computational studies in combinatorial problem solving using the polyhedral theory developed in the past fifteen years are surveyed: one addresses the symmetric traveling salesman p...

the probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. here we illustrate that a wider context may be considered and show some structural restrictions on the group.