The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Order Structure on the Algebra of Permutations and of Planar Binary Trees
Journal of Algebraic Combinatorics: An International Journal
Applied Combinatorics
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We find the winning strategy for a class of truncation games played on words. As a consequence of the present author's recent results on some of these games we obtain new formulas for Bernoulli numbers and polynomials of the second kind and a new combinatorial model for the number of connected permutations of given rank. For connected permutations, the decomposition used to find the winning strategy is shown to be bijectively equivalent to King's decomposition, used to recursively generate a transposition Gray code of the connected permutations.