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Pattern avoidance in compositions and multiset permutations
Carla D. Savage, Herbert S. Wilf
We study pattern avoidance by combinatorial objects other than permutations, namely by ordered partitions of an integer and by permutations of a multiset. In the former case we det…
The Redheffer matrix of a partially ordered set
Herbert S. Wilf
R. Redheffer described an matrix of 0's and 1's the size of whose determinant is connected to the Riemann Hypothesis. We describe the permutations that contribute to it…
The method of characteristics, and "problem 89" of Graham, Knuth and Patashnik
Herbert S. Wilf
We apply the method of characteristics for the solution of pde's to two combinatorial problems. The first is finding an explicit form for a distribution that arises in bio-informat…
Closed form summation of C-finite sequences
Curtis Greene, Herbert S. Wilf
We consider sums of the form \[\sum_{j=0}^{n-1}F_1(a_1n+b_1j+c_1)F_2(a_2n+b_2j+c_2)... F_k(a_kn+b_kj+c_k),\] in which each is a sequence that satisfies a linear recurr…
Irreducible compositions and the first return to the origin of a random walk
Edward A. Bender, Gregory F. Lawler, Robin Pemantle +1
Let be a pair of compositions of into positive parts. We say this pair is {\em irreducible} if there is no positive for…