rewrite content and config

4 files changed, 95 insertions, 0 deletions

diff --git a/content/research/_index.md b/content/research/_index.md
new file mode 100644
index 0000000..653425c
--- /dev/null
+++ b/content/research/_index.md
@@ -0,0 +1,6 @@
+---
+title: "Research"
+math: true
+---
+
+Various pieces of my academic research.
diff --git a/content/research/honors.md b/content/research/honors.md
new file mode 100644
index 0000000..c776e5a
--- /dev/null
+++ b/content/research/honors.md
@@ -0,0 +1,13 @@
+---
+title: "Analysis of Total Domination Algorithms on Graphs"
+date: 2023-12-18T00:48:31-05:00
+abstract: "An Abstract"
+summary: "My Senior Honors Project"
+description: "My Senior Honors Project"
+categories:
+tags:
+- "Graph Theory"
+- "Computational Complexity"
+---
+
+My Senior Honors Project from Spring to Fall 2024.
diff --git a/content/research/networks.md b/content/research/networks.md
new file mode 100644
index 0000000..b89fce7
--- /dev/null
+++ b/content/research/networks.md
@@ -0,0 +1,33 @@
+---
+title: "Network Reliability Parameters"
+date: 2023-12-18T00:21:27-05:00
+abstract: >
+    Let $G=(V,E)$ be a finite undirected graph with no isolated vertices.
+    A set $S \subseteq V$ is said to be a total dominating set of $G$ if every vertex in $V$ is adjacent to some vertex in $S$.
+    The total domination number, $\gamma_{t}(G)$, is the minimum cardinality of a total dominating set in $G$.
+    We define the $k$-total bondage to be the minimum number of edges to remove from $G$ so that the resulting graph has a total dominating number at least $k$ more than $\gamma_{t}(G)$.
+    In this work we establish general properties of $k$-total bondage, exact values for certain graph classes including paths, cycles, and wheels, and obtain upper bounds for complete and complete bipartite graphs.
+summary: "$k$-total bondage of Graphs"
+description: "Brief Description of Research"
+math: true
+categories:
+- "Moravian REU 2023"
+tags:
+- "Graph Theory"
+- "Combinatorics"
+---
+
+Peer Researchers
+: Gabriel Fischberg
+: Kyle Kelley
+: Eliel Sosis
+
+Mentors
+: Dr. Nathan Shank
+
+{{< presentations >}}
+## Presentations
+
+* Poster Sessions
+    * [Mathfest 2023](/research/posters/networks_mathfest23.pdf)
+{{< /presentations >}}
diff --git a/content/research/toggle.md b/content/research/toggle.md
new file mode 100644
index 0000000..6e29ce0
--- /dev/null
+++ b/content/research/toggle.md
@@ -0,0 +1,43 @@
+---
+title: "Exploring Toggle Games on Graphs"
+date: 2023-12-17T23:27:37-05:00
+summary: "Study of *Toggle*, an impartial game"
+abstract: >
+    In the commercial one-player game Lights Out™ a grid of lights is randomly generated with some lights on and some lights off.
+    The player can press a light to flip its on/off state as well as the state of its neighbors.
+    Toggle seeks to transform Lights Out™ into a variety of impartial two-player games.
+    Two players take turns toggling the on/off state of lights in an attempt to leave the other player with no available legal moves.
+    We analyze Toggle on various finite simple graphs and use impartial game theory to determine which player has a winning strategy given an initial Toggle configuration.
+    Finally, we prove that determining the winning player given an arbitrary Toggle configuration is PSpace-complete.
+categories:
+- "Moravian REU 2023"
+tags:
+- "Combinatorics"
+- "Game Theory"
+- "Computational Complexity"
+---
+
+Peer Researchers
+: [Nathan Hurtig](https://nathanhurtig.com/)
+: *Djenaba Djeob*
+
+Mentors
+: Dr. Eugene Fiorini
+: Dr. Andrew Woldar
+: Dr. Patrick Cesarz
+
+{{< presentations >}}
+## Presentations
+
+* Poster
+    * [SACNAS NDiSTEM 2023](/research/posters/toggle_ndistem23.pdf)
+{{< /presentations >}}
+
+
+{{< publications >}}
+## Publications
+
+* [A363934](https://oeis.org/A363934) Table read by ascending antidiagonals. T(n,k) is the Sprague-Grundy value for the Heat Toggle game played on an n X k grid where each vertex has initial weight 1. 
+* [A364489](https://oeis.org/A364489) Values of n for which the Sprague-Grundy value of Heat-Charge Toggle on an (n+2)-vertex path with initial weights -1,1^n,-1 is evil for odd n or odious for even n.
+* [A364503](https://oeis.org/A364503) Sprague-Grundy values for Heat-Charge Toggle on paths from A364489 where paths with an even number of vertices are odious, or paths with an odd number of vertices are evil.
+{{< /publications >}}