From 89501f368435383f8ac95479c4c92ed2d3e46e5d Mon Sep 17 00:00:00 2001 From: Oliver Date: Thu, 16 Jul 2020 21:45:09 -0400 Subject: [PATCH] minor --- poly-form.tex | 6 ------ 1 file changed, 6 deletions(-) diff --git a/poly-form.tex b/poly-form.tex index 1bb30ce..1591b90 100644 --- a/poly-form.tex +++ b/poly-form.tex @@ -110,16 +110,10 @@ When we expand $\poly(\wElem_1,\ldots, \wElem_N) = q_E(\wElem_1,\ldots, \wElem_\ \end{align} \end{Lemma} \AH{\cref{lem:qE3-exp} needs to be proven. I think I might need a gentle nudge on this, I can understand intuitively, but I think there is a combinatorics argument to prove this formally, I'm just a bit unsure.} -\OK{It's ugly, but I think this may just be an enumeration of cases. I might suggest showing first that this is all possible "shapes" of ways to pick 3 random edges from E, then extending the proof to show how edge counting maps to the polynomial $q_E$.} \AH{The warm-up below is fine for now, but will need to be removed for the final draft} First, let us do a warm-up by computing $\rpoly(\wElem_1,\dots, \wElem_\numTup)$ when $\poly = q_E(\wElem_1,\ldots, \wElem_\numTup)$. Before doing so, we introduce a notation. Let $\numocc{G}{H}$ denote the number of occurrences that $H$ occurs in $G$. So, e.g., $\numocc{G}{\ed}$ is the number of edges ($m$) in $G$. \AH{We need to make a decision on subgraph notation, and number of occurrences notation. Waiting to hear back from Oliver before making a decision.} - -\OK{ - I'm not sure what I can add. The existing notation is fine (for now). I would suggest adding - a definition table. -} \AH{UPDATE: I did a quick google, and it \textit{appears} that there is a bit of a learning curve to implement node/edge symbols in LaTeX. So, maybe, if time is of the essence, we go with another notation.} \begin{Claim}