Book Review: Combinatorial enumeration

Combinatorial Polytope Enumeration

We describe a provably complete algorithm for the generation of a tight, possibly exact, superset of all combinatorially distinct simple n-facet polytopes in Rd, along with their graphs, f -vectors, and face lattices. The technique applies repeated cutting planes and planar sweeps to a d−simplex. Our generator has implications for several outstanding problems in polytope theory, including conje...

Book Review

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Fast Enumeration of Combinatorial Objects

The problem of ranking (or perfect hashing) is well known in Combinatorial Analysis, Computer Science, and Information Theory. There are widely used methods for ranking permutations of numbers {1, 2, ..., n}, n ≥ 1, for ranking binary words of length n with a fixed number of ones and for many other combinatorial problems. Many of these methods have nonexponential memory size and the time of enu...

Book Review

book review