12 citations · 15 across the 8 of their papers we have counts for
14 papers
Maximal chains in lattices from graph associahedra: Tamari to the weak order
Samantha Dahlberg, Susanna Fishel
In this paper, we study the maximal chains of lattices which generalizes both the weak order and the Tamari lattice: certain lattices of maximal tubings. A maximal tubing poset $\m…
A Polynomial Method for Counting Colorings of Sparse Graphs
Samantha L. Dahlberg, Hemanshu Kaul, Jeffrey A. Mudrock
The notion of -labeling of graphs, where is a subset of a symmetric group, was introduced in 2019 by Jin, Wong, and Zhu. This notion provides the framework for a common gene…
An Algebraic Approach for Counting DP-3-colorings of Sparse Graphs
Samantha L. Dahlberg, Hemanshu Kaul, Jeffrey A. Mudrock
DP-coloring (or correspondence coloring) is a generalization of list coloring that has been widely studied since its introduction by Dvořák and Postle in 2015. As the analogue of t…
Diameters of Graphs on Reduced Words of 12 and 21-Inflations
Samantha Dahlberg, Younghwan Kim
It is a classical result that any permutation in the symmetric group can be generated by a sequence of adjacent transpositions. The sequences of minimal length are called reduced w…
Chromatic Posets
Samantha Dahlberg, Adrian She, Stephanie van Willigenburg
In 1995 Stanley introduced the chromatic symmetric function of a graph , whose -positivity and Schur-positivity has been of large interest. In this paper we study the r…
Chromatic symmetric functions in noncommuting variables revisited
Samantha Dahlberg, Stephanie van Willigenburg
In 1995 Stanley introduced a generalization of the chromatic polynomial of a graph , called the chromatic symmetric function, , which was generalized to noncommuting variab…
Schur and -positivity of trees and cut vertices
Samantha Dahlberg, Adrian She, Stephanie van Willigenburg
We prove that the chromatic symmetric function of any -vertex tree containing a vertex of degree is not -positive, that is, not a positive linear combinat…
Triangular Ladders are -positive
Samantha Dahlberg
In 1995 Stanley conjectured that the chromatic symmetric functions of the graphs , which we call triangular ladders, were -positive. In this paper we confirm this conje…
Permutation Statistics and Pattern Avoidance in Involutions
Samantha Dahlberg
Dokos et. al. studied the distribution of two statistics over permutations of that avoid one or more length three patterns. A permutation $σ\in\…
Resolving Stanley's -positivity of claw-contractible-free graphs
Samantha Dahlberg, Angele Foley, Stephanie van Willigenburg
In Stanley's seminal 1995 paper on the chromatic symmetric function, he stated that there was no known graph that was not contractible to the claw and whose chromatic symmetric fun…
Lollipop and lariat symmetric functions
Samantha Dahlberg, Stephanie van Willigenburg
We compute an explicit -positive formula for the chromatic symmetric function of a lollipop graph, . From here we deduce that there exist countably infinite distinct $e…
Restricted growth function patterns and statistics
Lindsey R. Campbell, Samantha Dahlberg, Robert Dorward +4
A restricted growth function (RGF) of length n is a sequence w = w_1 w_2 ... w_n of positive integers such that w_1 = 1 and w_i is at most 1 + max{w_1,..., w_{i-1}} for i at least…
Set partition patterns and statistics
Samantha Dahlberg, Robert Dorward, Jonathan Gerhard +4
A set partition of contains another set partition if restricting to some and then standardizing the result gives . Otherwise we s…
Combinatorial Proofs of Identities Involving Symmetric Matrices
Samantha Dahlberg
Brualdi and Ma found a connection between involutions of length with descents and symmetric matrices with non-negative integer entries summing to and having…