11 citations · 50 across the 20 of their papers we have counts for
14 papers · 1 filter
Ramanujan sums and rectangular power sums
John Shareshian, Sheila Sundaram
For a fixed nonnegative integer and positive integer , we investigate the symmetric function \[\sum_{d|n} \left(c_d(\tfrac{n}{d})\right)^u p_d^{\tfrac{n}{d}},\] where …
Moments of Colored Permutation Statistics on Conjugacy Classes
Jesse Campion Loth, Michael Levet, Kevin Liu +2
In this paper, we consider the moments of statistics on conjugacy classes of the colored permutation groups . We first show that…
Topology of Cut Complexes of Graphs
Margaret Bayer, Mark Denker, Marija Jelić Milutinović +3
We define the -cut complex of a graph with vertex set to be the simplicial complex whose facets are the complements of sets of size in inducing disconnecte…
Permutation Statistics in Conjugacy Classes of the Symmetric Group
Jesse Campion Loth, Michael Levet, Kevin Liu +3
We introduce the notion of a weighted inversion statistic on the symmetric group, and examine its distribution on each conjugacy class. Our work generalizes the study of several co…
Pieri rules for skew dual immaculate functions
Elizabeth Niese, Sheila Sundaram, Stephanie van Willigenburg +1
In this paper we give Pieri rules for skew dual immaculate functions and their recently discovered row-strict counterparts. We establish our rules using a right-action analogue of…
On Sums, Derivatives, and Flips of Riordan Arrays
Caroline Bang, Matias von Bell, Eric Culver +4
We study three operations on Riordan arrays. First, we investigate when the sum of Riordan arrays yields another Riordan array. We characterize the - and -sequences of these…
Total Cut Complexes of Graphs
Margaret Bayer, Mark Denker, Marija Jelić Milutinović +3
Inspired by work of Fröberg (1990), and Eagon and Reiner (1998), we define the \emph{total -cut complex} of a graph to be the simplicial complex whose facets are the complem…
0-Hecke modules for row-strict dual immaculate functions
Elizabeth Niese, Sheila Sundaram, Stephanie van Willigenburg +2
We introduce a new basis of quasisymmetric functions, the row-strict dual immaculate functions. We construct a cyclic, indecomposable 0-Hecke algebra module for these functions. Ou…
Row-strict dual immaculate functions
Elizabeth Niese, Sheila Sundaram, Stephanie van Willigenburg +2
We define a new basis of quasisymmetric functions, the row-strict dual immaculate functions, as the generating function of a particular set of tableaux. We establish that this defi…
The plethystic inverse of the odd Lie representations
Sheila Sundaram
The Frobenius characteristic of the representation of the symmetric group afforded by the multilinear component of the free Lie algebra, is known to satisfy many int…
On a positivity conjecture in the character table of
Sheila Sundaram
In previous work of this author it was conjectured that the sum of power sums for partitions ranging over an interval in reverse lexicographic order, is Sch…
Some Problems Arising from Partition Poset Homology
Sheila Sundaram
We describe some open problems related to homology representations of subposets of the partition lattice, beginning with questions first raised in Stanley's work on group actions o…
Counting permutations by congruence class of major index
Helene Barcelo, Bruce Sagan, Sheila Sundaram
Consider S_n, the symmetric group on n letters, and let maj pi denote the major index of a permutation pi in S_n. Given positive integers k,l and nonnegative integers i,j, define m…
On counting permutations by pairs of congruence classes of major index
Helene Barcelo, Robert Maule, Sheila Sundaram
For a fixed positive integer n, let S_n denote the symmetric group of n! permutations on n symbols, and let maj(sigma) denote the major index of a permutation sigma. For positive i…