8 papers · 1 filter
On the Graph Laplacian and the Rankability of Data
Thomas R. Cameron, Amy N. Langville, Heather C. Smith
Recently, Anderson et al. (2019) proposed the concept of rankability, which refers to a dataset's inherent ability to produce a meaningful ranking of its items. In the same paper,…
Improved bounds for induced poset saturation
Ryan R. Martin, Heather C. Smith, Shanise Walker
Given a finite poset , a family of elements in the Boolean lattice is induced--saturated if contains no copy of …
Planar Posets that are Accessible from Below Have Dimension at Most 6
Csaba Biró, Bartłomiej Bosek, Heather C. Smith +3
Planar posets can have arbitrarily large dimension. However, a planar poset of height has dimension at most , while a planar poset with minimal elements has dimens…
Fractional Local Dimension
Heather C. Smith, William T. Trotter
The original notion of dimension for posets was introduced by Dushnik and Miller in 1941 and has been studied extensively in the literature. In 1992, Brightwell and Scheinerman dev…
On difference graphs and the local dimension of posets
Jinha Kim, Ryan R. Martin, Tomáš Masařík +4
The dimension of a partially-ordered set (poset), introduced by Dushnik and Miller (1941), has been studied extensively in the literature. Recently, Ueckerdt (2016) proposed a vari…
On Edge-Colored Saturation Problems
Michael Ferrara, Daniel Johnston, Sarah Loeb +6
Let be a family of edge-colored graphs. A -edge colored graph is -saturated if does not contain any graph in but the additi…