10 citations · 16 across the 7 of their papers we have counts for
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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…
The combinatorics of a three-line circulant determinant
Nicholas A. Loehr, Gregory S. Warrington, Herbert S. Wilf
We study the determinant of the pxp circulant matrix whose first row is (1,-x,0,...,0,-y,0,...,0), the -y being in position q+1. The coefficients of this polynomial are integers th…
A Discontinuity in the Distribution of Fixed Point Sums
Edward A. Bender, E. Rodney Canfield, L. Bruce Richmond +1
The quantity , defined as the number of permutations of the set whose fixed points sum to , shows a sharp discontinuity in the neighborhood of .…