Lattice Path Combinatorics and Applications

This is a collection of more than a dozen papers covering most areas of lattice path combinatorics. The book contains research articles, expository papers, and several historical overviews and commemorative articles. 

 

The editors did a good job to select papers from analytic combinatorics (the kernel method, asymptotic estimates), algebraic combinatorics (cycle counting, wreath products), bijective combinatorics (Schroeder structures, parking functions), q-analogues, number theory (integer partitions), and probability (Gambler's ruin). 

 

Applications are represented by two papers on the theory of queues. The only subject that this reviewer regretted not finding in the book was injective proofs using lattice paths. An index would have been nice as well. However, these are minor issues; this reviewer found most articles in the collection well-written and readable. Most enumerative combinatorialists will like at least a few of them.

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Miklós Bóna is a Professor and Distinguished Teaching Scholar at the University of Florida, and the author and editor of several books. His main research interest is Enumerative Combinatorics.