20 citations · 32 across the 10 of their papers we have counts for
10 papers · 1 filter
Restricted k-color partitions, II
William J. Keith
We consider -colored partitions, partitions in which colors exist but at most colors may be chosen per size of part. In particular these generalize overpartitions. A…
Binary compositions and semi-Pell compositions
William J. Keith, Augustine O. Munagi
In analogy with the semi-Fibonacci partitions studied recently by Andrews, we define semi-Pell compositions and semi--Pell compositions. We find that these are in bijection with…
Partitions into parts simultaneously regular, distinct, and/or flat
William J. Keith
We explore partitions that lie in the intersection of several sets of classical interest: partitions with parts indivisible by , appearing fewer than times, or differing by…
Colored partitions and the hooklength formula: partition statistic identities
Emily E. Anible, William J. Keith
We give relations between the joint distributions of multiple hook lengths and of frequencies and part sizes in partitions, extending prior work in this area. These results are dis…
Families of major index distributions: closed forms and unimodality
William J. Keith
Closed forms for , the distribution of the major index over standard Young tableaux of given shapes and specified number…
Major index over descent for pattern-avoiding permutations
William J. Keith
An open conjecture in pattern avoidance theory is that the distribution of the major index among 321-avoiding permutations is distributed unimodally. We construct a formula for thi…