A recent paper (Edman et al. [6]) has taken a combinatorial approach to measuring the anonymity of a threshold mix anonymous communications system. Their paper looks at ways of matching individual messages sent to individual messages received, irrespective of user, and determines a measure of the anonymity provided by the system. Here we extend this approach to include in the calculation inform...

An algorithm for creating repeating patterns from a single decorated square gives rise to an obvious combinatorial question: How many different patterns can be created, following the rules? Answers vary according to the definition of equivalence of patterns, and computer sorting programs can provide numerical answers. But algebraic techniques give insight into the answers and provide general fo...

The well-known vertex enumeration problem calls for generating all vertices of a polyhedron, given by its description as a system of linear inequalities. Recently, a number of combinatorial techniques have been developed and applied successfully to a large number of monotone generation problems in different areas. We consider four such techniques and give examples where they are applicable to v...

Abstract: Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are related to certain configurations of vicious random walkers and to the enumeration of plane partitions. The combinatorial meaning of the average of the c...

Constraint Programming (CP) is a powerful paradigm for solving Combinatorial Problems (generally issued from Decision Making). In CP, Enumeration Strategies are crucial for resolution performances. In this work, we model the known benchmark problems Latin Square, Magic Square and Sudoku as a Constraint Satisfaction Problems. We solve them with Constraint Programming comparing the performance of...

The well-known vertex enumeration problem calls for generating all vertices of a polyhedron, given by its description as a system of linear inequalities. Recently, a number of combinatorial techniques have been developed and applied successfully to a large number of monotone generation problems in different areas. We consider four such techniques and give examples where they are applicable to v...

This report is a comprehensive review of the field of molecular enumeration from early isomer counting theories to evolutionary algorithms that design molecules in silico. The core of the review is a detail account on how molecules are counted, enumerated, and sampled. The practical applications of molecular enumeration are also reviewed for chemical information, structure elucidation, molecula...

Let A be a class of objects, equipped with an integer size such that for all n the number an of objects of size n is finite. We are interested in the case where the generating function ∑ n ant n is rational, or more generally algebraic. This property has a practical interest, since one can usually say a lot on the numbers an, but also a combinatorial one: the rational or algebraic nature of the...