2 citations · 4 across the 4 of their papers we have counts for
4 papers
A Simple Proof that Major Index and Inversions are Equidistributed
Michael J. Collins
We present a short proof of MacMahon's classic result that the number of permutations with inversions equals the number whose major index (sum of positions at which descents oc…
Equivalence of OEIS A007729 and A174868
Michael J. Collins, David Wilson
We verify the conjecture that the sixth binary partition function is equal (aside from the initial zero term) to the partial sums of the Stern-Brocot sequence.
The Number of Distinct Subsequences of a Random Binary String
Michael J. Collins
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
Modular analogues of Jordan's theorem for finite linear groups
Michael J. Collins
In 1878, Jordan showed that a finite subgroup of GL(n,C) contains an abelian normal subgroup whose index is bounded by a function of n alone. Previously, the author has given preci…