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0 "" {MPLTEXT 1 0 8 "op(SGJ);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#R6%%
\"nG%*MISTAKES1G%\"sG6*%\"vG%#eqG%$varG%\"iG%#luG%\"CG%)MISTAKESG%$ans
G6\"F1C+>8*-%'HaktenG6#9%>8%<\">8&F;?(8'\"\"\"F@-%%nopsG6#F4%%trueGC%>
8$-%#opG6$F?F4>F:-%&unionG6$F:<#-%(findeqzG6&FGF48)9&>F=-FM6$F=<#&FS6#
-FI6#FG>F=-%&solveG6$F:F=>8(,&F@F@*&FTF@9$F@!\"\"?(F?F@F@FAFDC$>FGFH>F
\\o,&F\\oF@-%%subsG6$F=FYF`o>8+-%'normalG6#*&F@F@F\\oF`o*&-%(collectG6
$-%&numerG6#FjoFTF@-Fap6$-%&denomGFepFTF`oF1F1F1" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 246 "MISTAKES := Hakten(\{[1,2,3],[1,3,2],[2,1,3]
,[2,3,1],[3,1,2],[3,2,1]\}); eq := \{\}; var := \{\}; for i to nops(MI
STAKES) do v := op(i,MISTAKES); eq := `union`(eq,\{findeqz(v,MISTAKES,
C,s)\}); var := `union`(var,\{C[op(v)]\}) end do; var := solve(eq,var)
; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)MISTAKESG<(7%\"\"\"\"\"#\"\"$
7%F(F)F'7%F)F'F(7%F'F)F(7%F(F'F)7%F)F(F'" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#eqG<\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$varG<\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG7%\"\"\"\"\"#\"\"$" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%#eqG<#/,,&%\"CG6%\"\"\"\"\"#\"\"$F+*$)%\"sGF-F
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\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$varG<#&%\"CG6%\"\"\"\"\"#
\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG7%\"\"#\"\"$\"\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG<$/,,&%\"CG6%\"\"\"\"\"#\"\"$F+*
$)%\"sGF-F+F+*&)F0F,F+&F)6%F,F-F+F+F+*&F0F+&F)6%F-F+F,F+F+*&F2F+&F)6%F
-F,F+F+F+\"\"!/,,F3F+F.F+*&F0F+F(F+F+*&F2F+F6F+F+*&F2F+&F)6%F+F-F,F+F+
F;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$varG<$&%\"CG6%\"\"\"\"\"#\"\"
$&F'6%F*F+F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG7%\"\"$\"\"\"\"
\"#" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#eqG<%/,,&%\"CG6%\"\"\"\"\"#
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F+&F)6%F-F,F+F+F+\"\"!/,,F3F+F.F+*&F0F+F(F+F+*&F2F+F6F+F+*&F2F+&F)6%F+
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}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$varG<%&%\"CG6%\"\"\"\"\"#\"\"$&F'
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\"\"$\"\"#" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#eqG<&/,,&%\"CG6%\"\"
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+F+*&F2F+&F)6%F-F,F+F+F+\"\"!/,,F3F+F.F+*&F0F+F(F+F+*&F2F+F6F+F+*&F2F+
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+F+F;/,,FAF+F.F+F1F+*&F0F+FHF+F+F8F+F;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$varG<&&%\"CG6%\"\"\"\"\"#\"\"$&F'6%F*F+F)&F'6%F+F)F*&F'6%F)F+
F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG7%\"\"#\"\"\"\"\"$" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#eqG<'/,,&%\"CG6%\"\"\"\"\"#\"\"$F+*
$)%\"sGF-F+F+*&)F0F,F+&F)6%F,F-F+F+F+*&F0F+&F)6%F-F+F,F+F+*&F2F+&F)6%F
-F,F+F+F+\"\"!/,,F3F+F.F+*&F0F+F(F+F+*&F2F+F6F+F+*&F2F+&F)6%F+F-F,F+F+
F;/,,F6F+F.F+*&F2F+F(F+F+*&F0F+F3F+F+*&F2F+&F)6%F,F+F-F+F+F;/,,FAF+F.F
+F1F+*&F0F+FHF+F+F8F+F;/,,FHF+F.F+F?F+F@F+*&F0F+F9F+F+F;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%$varG<'&%\"CG6%\"\"\"\"\"#\"\"$&F'6%F*F+F)&F'6
%F+F)F*&F'6%F)F+F*&F'6%F*F)F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"v
G7%\"\"$\"\"#\"\"\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#eqG<(/,,&%\"
CG6%\"\"\"\"\"#\"\"$F+*$)%\"sGF-F+F+*&)F0F,F+&F)6%F,F-F+F+F+*&F0F+&F)6
%F-F+F,F+F+*&F2F+&F)6%F-F,F+F+F+\"\"!/,,F3F+F.F+*&F0F+F(F+F+*&F2F+F6F+
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%F,F+F-F+F+F;/,,FAF+F.F+F1F+*&F0F+FHF+F+F8F+F;/,,FHF+F.F+F?F+F@F+*&F0F
+F9F+F+F;/,,F9F+F.F+FEF+*&F0F+FAF+F+FGF+F;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$varG<(&%\"CG6%\"\"\"\"\"#\"\"$&F'6%F*F+F)&F'6%F+F)F*
&F'6%F)F+F*&F'6%F*F)F+&F'6%F+F*F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>
%$varG<(/&%\"CG6%\"\"$\"\"#\"\"\",$*&*$)%\"sGF*F,F,,(*$)F1F+F,F+F1F,F,
F,!\"\"F5/&F(6%F+F*F,F-/&F(6%F*F,F+F-/&F(6%F+F,F*F-/&F(6%F,F+F*F-/&F(6
%F,F*F+F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "SSGJ(n,[[1,2,3
],[1,1]],s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*&,&%\"nG\"\"#*$)F
'F(\"\"\"!\"\"F+)%\"sGF(F+F+*&,&F'F,F+F+F+F.F+F+F+F,F+,&F,F+F.F+F," }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ezra(SAW_SSGJ);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%7SAW_SSGJ(n,MISTAKES,s)G" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%>Finding~generating~functions~G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%enfor~the~number~of~words,~in~the~alphabet~-1,1,-2,2,.
.,-d,dG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%R~avoiding~a~prescribed,~f
inite,~set~of~\"MISTAKES\"G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%inthe~
set~of~mistakes~is~closed~under~the~action~of~the~group~ofG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%4signed~permutationsG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%[oFor~example~to~get~the~g.f.~for~a_m:=number~of~words
~of~length~mG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%goin~the~alphabet~|f
r-1,1,-2,2,-3,3,...,-n,n|hr,~2~memory~self~avoiding~walk,type~G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%9~SAW_SSGJ(n,[[1,-1]],s);G" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "a:=SAW_SSGJ(n,[[1,-1]],s);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG*&,&!\"\"\"\"\"%\"sGF'F(,&*&,&
F'F(*&\"\"#F(%\"nGF(F(F(F)F(F(F(F'F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "subs(n=4,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,
&!\"\"\"\"\"%\"sGF%F&,&F'\"\"(F&F%F%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 45 "b:=SSGJ(n,[[1,1],[1,2,2,3],[1,2,3,3,2,3]],s);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "IsIsoSubString([1,2,3],[2,3]
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "eq1:=findequ(n,[1,1],
[[1,1],[1,2,1,2]],s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "eq
2:=findequ(n,[1,1,1],[[1,1,1],[1,1]],s);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "eq2 := C(1,1,1) = -s^3-C(1,2,3)*s^2;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "solve(\{eq1,eq2\},\{C(1,1,1),C(1,1)
\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "trace(smblsymgj);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?cont" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 41 "kernalarr([[1,2,3],[2,3,1],[1,1],[2,2]]);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?expand" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 3 "?ta" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 38 "GetOffIsoSupstring([[1,1],[1,2,2,1]]);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 35 "kernalarr([[2,3,1],[3,2,1],[1,1]]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "issubword([1,2,3,4],[2,3,1]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "superflous(\{[1,2,3],[0,1,2,
3,4]\},[1,2,3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Hakten(
\{[1,2,3],[0,1,2,3,4]\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "hakten1(\{[0,1,2,3,4],[1,2,3]\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "overlapz([1,2,3,4],[3,4,5],s);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 39 "findeqz([1,2,3],\{[1,2,3],[1,1,1]\},C,s);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "saw_findequ(n,[1,2,3],[[1,2,
3],[1,1]],s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"CG6%\"\"\"\"\"#
\"\"$,**$)%\"sGF)F'!\"\"*(F$F',&%\"nGF'F(F.F'F-F'F.**F$F',&F1F'F'F.F'F
0F')F-F(F'F.*&-F%6$F'F'F'F4F'F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 39 "saw_isostring([-1,2,1,-2],[2,-1,-2,1]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "ab
s(-a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$absG6#%\"aG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "saw_kernal([1,-1,2,-2,-3,3,-4,4,5,-
1,1,6]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(\"\"\"\"\"#!\"$!\"%\"\"&
\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "a:=saw_SSGJ(n,[[1,
-1],[1,2,-1,-2]],s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG*&,**&,&
%\"nG!\"#\"\"\"F+F+)%\"sG\"\"$F+F+*&\"\"#F+)F-F0F+!\"\"*&F0F+F-F+F2F+F
2F+,**$F,F+F+*&,&F)F0F0F2F+F1F+F+*&F7F+F-F+F+F+F2F2" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 22 "taylor(subs(n=4,a),s);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#+1%\"sG\"\"\"\"\"!\"\")F%\"#c\"\"#\"$#R\"\"$\"%WF\"\"
%\"&3#>\"\"&-%\"OG6#F%\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "subs(n=5,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"sG\"\")\"\"
\"F'F',(*$)F%\"\"#F'\"#S*&\"\"$F'F%F'F'F'F'!\"\"" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 33 "saw_findequ(n,[1,-1],[[1,-1]],s);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%\"CG6$\"\"\"!\"\",&*$)%\"sG\"\"#F'F(*&F$F
'F,F'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "trace(saw_findeq
u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%,saw_findequG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "saw_kernal([1,2,-1]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7$\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "nops(saw_kernal([1,2,-1]))-nops(saw_kernal([1,2]));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "13 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
1 1 }{PAGENUMBERS 0 1 2 33 1 1 }