From 56b740565fd6467564be28b5465ad24cccf71109 Mon Sep 17 00:00:00 2001
From: Holden Rohrer <hr@hrhr.dev>
Date: Thu, 16 Jan 2020 21:24:46 -0500
Subject: moved comb hw

---
 tech-math/comb/ws6.tex | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)
 create mode 100644 tech-math/comb/ws6.tex

(limited to 'tech-math/comb/ws6.tex')

diff --git a/tech-math/comb/ws6.tex b/tech-math/comb/ws6.tex
new file mode 100644
index 0000000..5042920
--- /dev/null
+++ b/tech-math/comb/ws6.tex
@@ -0,0 +1,29 @@
+\def\pre#1{\leavevmode\llap{\hbox to \parindent{\hfil #1 \hfil}}}
+
+\noindent {\bf Q1)} %#14:2
+
+Considering a flow from Source $S$ which is connected to all members of $V_1$ and a similar sink $T$ with respect to $V_2$, this can be solved by the Ford-Fulkerson algorithm. 
+
+Let $V_{kj}$ be the $j^{th}$ member, from left to right of $V_k$. The optimum matching is $$\{V_11\to V_22, V_12\to V_27, V_13\to V_25, V_14\to V_21, V_15\to V_26, V_17\to V_24\}$$ because the Ford-Fulkerson algorithm halts, and Hall's theorem holds: there is a grouping of vertices in $V_1$ with a fewer number of neighbors than in the group.
+
+\noindent {\bf Q2)} %#14:8
+
+$w=3$.
+
+Antichain: $\{x_1,x_2,x_3\}$.
+
+Chain Partition: $\{x_3,x_4,x_5\}\cup\{x_6,x_1\}\cup\{x_2\}$.
+
+\noindent {\bf Q3)} %#15:2
+
+\let\sp\thinspace
+$$\pi_1\pi_2 = \left({1\sp 2\sp 3\sp 4\sp 5\sp 6 \atop
+                      3\sp 6\sp 4\sp 2\sp 1\sp 5}\right)$$
+$$\pi_2\pi_1 = \left({1\sp 2\sp 3\sp 4\sp 5\sp 6 \atop
+                      3\sp 1\sp 4\sp 5\sp 6\sp 2}\right)$$
+$$\pi_3\pi_4 = \left({1\sp 2\sp 3\sp 4\sp 5\sp 6\sp 7\sp 8 \atop
+                      1\sp 3\sp 8\sp 5\sp 7\sp 4\sp 6\sp 2}\right)$$
+$$\pi_4\pi_3 = \left({1\sp 2\sp 3\sp 4\sp 5\sp 6\sp 7\sp 8 \atop
+                      5\sp 4\sp 3\sp 6\sp 7\sp 8\sp 1\sp 2}\right)$$
+
+\bye
-- 
cgit 

