6 research outputs found
The Asymptotic Number of Irreducible Partitions
A partition of [1, n] = {1,..., n} is called irreducible if no proper subinterval of [1, n] is a union of blocks. We determine the asymptotic relationship between the numbers of irreducible partitions, partitions without singleton blocks, and all partitions when the block sizes must lie in some specified set
Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions
We find Stieltjes-type and Jacobi-type continued fractions for some "master
polynomials" that enumerate permutations, set partitions or perfect matchings
with a large (sometimes infinite) number of simultaneous statistics. Our
results contain many previously obtained identities as special cases, providing
a common refinement of all of them.Comment: LaTeX2e, 122 pages, includes 9 tikz figure