Shen-Fu Tsai

activity

20172025

most citedSharper bounds and structural results for minimally nonlinear 0-1 matrices

4 citations · 6 across the 14 of their papers we have counts for

collaborators

Showing math.COShow all

10 papers · 1 filter

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

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 $u$ …

math.CO2023

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.CO2022

Saturation of multidimensional 0-1 matrices

Shen-Fu Tsai

A 0-1 matrix $M$ is saturating for a 0-1 matrix $P$ if $M$ does not contain a submatrix that can be turned into $P$ by flipping any number of its $1$ -entries to $0$ -entries, and ch…

math.CO2021

Peripherality in networks: theory and applications

Jesse Geneson, Shen-Fu Tsai

We investigate several related measures of peripherality and centrality for vertices and edges in networks, including the Mostar index which was recently introduced as a measure of…

math.CO2018★ 4 cited

Sharper bounds and structural results for minimally nonlinear 0-1 matrices

Jesse Geneson, Shen-Fu Tsai

The extremal function $e x (n, P)$ is the maximum possible number of ones in any 0-1 matrix with $n$ rows and $n$ columns that avoids $P$ . A 0-1 matrix $P$ is called minimally non-li…

math.CO2017

Computing optimal strategy for cop in the game of Cop v.s. Gambler

Shen-Fu Tsai

We present two efficient algorithms that compute the optimal strategy for cop in the game of Cop v.s. Gambler where the gambler's strategy is not optimal but known to the cop. The…

math.CO2017

Two properties of maximal antichains in strict chain product posets

Shen-Fu Tsai

We present two results on maximal antichains in the strict chain product poset $[t_{1} + 1] \times [t_{2} + 1] \times \dots \times [t_{n} + 1]$ . First, we prove that these maximal antichains are al…