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COMBINATORICS
2006
14 years 9 months ago
2006
This note deals with a formula due to G. Labelle for the summed cycle indices of all rooted trees, which resembles the well-known formula for the cycle index of the symmetric grou...
COMBINATORICS
2006
14 years 9 months ago
2006
We present a variation of James Propp's generalized domino shuffling, which provides an efficient way to obtain perfect matchings of weighted Aztec diamonds. Our modification...
COMBINATORICS
2006
14 years 9 months ago
2006
Let h, e, and m denote the homogeneous symmetric function, the elementary symmetric function and the monomial symmetric function associated with the partition respectively. We gi...
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COMBINATORICS
2006
14 years 9 months ago
2006
We define incidence matrices to be zero-one matrices with no zero rows or columns. We are interested in counting incidence matrices with a given number of ones, irrespective of th...
COMBINATORICS
2006
14 years 9 months ago
2006
Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square or...