Update 37a.md

Author: paatai

constants/37a.md

@@ -2,7 +2,11 @@
 
 ## Description of constant
 
-Let $f$ be a Boolean function on $n$ bits, i.e. $f:${0,1}^n $\to$ {0,1}
+Let $f$ be a Boolean function on $n$ bits, i.e. 
+
+$$
+f:\{0,1\}^n \to \{0,1\}
+$$
 
 with $n\ge 2$.
 For $x\in$ {0,1}^n and $1\le i\le n$, let $x^{(i)}$ be $x$ with the $i$-th bit flipped.
@@ -54,8 +58,11 @@ $$
 
 - The best known **explicit** exponent separating sensitivity from degree is currently $\log_3 6$ (the “Kushilevitz barrier”). Improving this exponent is an open problem.  “Kushilevitz function” was introduced (unpublished by Kushilevitz) in **Footnote 1 of Nisan and Wigderson’s paper** [NW95].
 
-- (Kushilevitz base.) One explicit polynomial representing the base function $h:\{0,1\}^6\to\{0,1\}$ is
-
+- (Kushilevitz base.) One explicit polynomial representing the base function 
+$$
+h:\{0,1\}^6\to\{0,1\}
+$$
+is
 $h(z_1,\dots,z_6)=\sum_{i=1}^6 z_i - \sum_{1\le i<j\le 6} z_i z_j + (z_1z_3z_4 + z_1z_2z_5 + z_1z_4z_5 + z_2z_3z_4 + z_2z_3z_5 + z_1z_2z_6 + z_1z_3z_6 + z_2z_4z_6 + z_3z_5z_6 + z_4z_5z_6),$
 
   which is Boolean on $\{0,1\}^6$, has degree $3$, and is fully sensitive at $(0,0,0,0,0,0)$.