Shen-Fu Tsai

collaborators

5 papers

math.CO2025

Pattern Forcing (0,1)-Matrices

Lei Cao, Shen-Fu Tsai

We introduce two related notions of pattern enforcement in $(0, 1)$ -matrices: $Q$ -forcing and strongly $Q$ -forcing, which formalize distinct ways a fixed pattern $Q$ must appear wit…

math.CO2025

Throttling for metric dimension and its variants

Boris Brimkov, Peter Diao, Jesse Geneson +4

Metric dimension is a graph parameter that has been applied to robot navigation and finding low-dimensional vector embeddings. Throttling entails minimizing the sum of two availabl…

math.CO2025

Fault tolerance for metric dimension and its variants

Jesse Geneson, Shen-Fu Tsai

Hernando et al. (2008) introduced the fault-tolerant metric dimension $ftdim (G)$ , which is the size of the smallest resolving set $S$ of a graph $G$ such that $S-\left\{s\ri…

math.CO2024

Extremal bounds for pattern avoidance in multidimensional 0-1 matrices

Jesse Geneson, Shen-Fu Tsai

A 0-1 matrix $M$ contains another 0-1 matrix $P$ if some submatrix of $M$ can be turned into $P$ by changing any number of $1$ -entries to $0$ -entries. $M$ is $P$ -saturate…

math.CO2024

Sequence saturation

Anand, Jesse Geneson, Suchir Kaustav +1

In this paper, we introduce saturation and semisaturation functions of sequences, and we prove a number of fundamental results about these functions. Given a forbidden sequence $u$ …