%defaultfont:="csr12";
%verbatimtex \input twelvecs etex
u:=1 ;
ahlength:=u*3;

beginfig(0);
v:=u*7mm;

z12=(1v,1v);
z13=(2v,1v);
z21=(0v,2v);
z22=(1v,2v);
z23=(2v,2v);
z24=(3v,2v);
z31=(0v,4v);
z32=(1v,4v);
z33=(2v,4v);
z34=(3v,4v);
z42=(1v,5v);
z43=(2v,5v);

pickup pencircle scaled 0.4pt;
draw(z21--z22--z23--z24--z34--z33--z32--z31--z21);
drawarrow(z22--z12);
drawarrow(z23--z13);
drawarrow(z42--z32);
drawarrow(z43--z33);

label.bot(btex \strut a etex,z32);
label.bot(btex \strut b etex,z33);
label.top(btex min etex,z22);
label.top(btex max etex,z23);


endfig;

beginfig(1);
v:=u*5mm;
z10=(0v,0v);
z20=(2v,0v);
z30=(4v,0v);
z40=(6v,0v);
z50=(8v,0v);

z11=(0v,1v);
z12=(0v,2v);
z13=(0v,3v);
z14=(0v,4v);
z15=(0v,5v);
z16=(0v,6v);
z17=(0v,7v);
z18=(0v,8v);
z19=(0v,9v);
z110=(0v,10v);

z21=(2v,1v);
z22=(2v,2v);
z23=(2v,3v);
z24=(2v,4v);
z25=(2v,5v);
z26=(2v,6v);
z27=(2v,7v);
z28=(2v,8v);
z29=(2v,9v);
z210=(2v,10v);

z31=(4v,1v);
z32=(4v,2v);
z33=(4v,3v);
z34=(4v,4v);
z35=(4v,5v);
z36=(4v,6v);
z37=(4v,7v);
z38=(4v,8v);
z39=(4v,9v);
z310=(4v,10v);

z41=(6v,1v);
z42=(6v,2v);
z43=(6v,3v);
z44=(6v,4v);
z45=(6v,5v);
z46=(6v,6v);
z47=(6v,7v);
z48=(6v,8v);
z49=(6v,9v);
z410=(6v,10v);

z51=(8v,1v);
z52=(8v,2v);
z53=(8v,3v);
z54=(8v,4v);
z55=(8v,5v);
z56=(8v,6v);
z57=(8v,7v);
z58=(8v,8v);
z59=(8v,9v);
z510=(8v,10v);

z111=(0v,11v);
z211=(2v,11v);
z311=(4v,11v);
z411=(6v,11v);
z511=(8v,11v);

z1015=(-1v,1.5v);
z1615=(9v,1.5v);
z1035=(-1v,3.5v);
z1635=(9v,3.5v);
z1065=(-1v,6.5v);
z1665=(9v,6.5v);

pickup pencircle scaled 0.4pt;
draw(z10--z111);
draw(z20--z211);
draw(z30--z311);
draw(z40--z411);
draw(z50--z511);
drawarrow(z11--z21);
drawarrow(z13--z23);
drawarrow(z16--z26);
drawarrow(z110--z210);
drawarrow(z22--z32);
drawarrow(z25--z35);
drawarrow(z29--z39);
drawarrow(z34--z44);
drawarrow(z38--z48);
drawarrow(z47--z57);

pickup pencircle scaled 0.7pt;
draw(z1015--z1615) dashed withdots scaled 0.7;
draw(z1035--z1635) dashed withdots scaled 0.7;
draw(z1065--z1665) dashed withdots scaled 0.7;

label.top(btex x1 etex,z111);
label.top(btex x2 etex,z211);
label.top(btex x3 etex,z311);
label.top(btex x4 etex,z411);
label.top(btex x5 etex,z511);

endfig;

beginfig(2);
v:=u*5mm;
z13=(0v,3v);
z23=(2v,3v);
z33=(4v,3v);
z43=(6v,3v);
z53=(8v,3v);

z14=(0v,4v);
z15=(0v,5v);
z16=(0v,6v);
z17=(0v,7v);
z18=(0v,8v);
z19=(0v,9v);
z110=(0v,10v);

z24=(2v,4v);
z25=(2v,5v);
z26=(2v,6v);
z27=(2v,7v);
z28=(2v,8v);
z29=(2v,9v);
z210=(2v,10v);

z34=(4v,4v);
z35=(4v,5v);
z36=(4v,6v);
z37=(4v,7v);
z38=(4v,8v);
z39=(4v,9v);
z310=(4v,10v);

z44=(6v,4v);
z45=(6v,5v);
z46=(6v,6v);
z47=(6v,7v);
z48=(6v,8v);
z49=(6v,9v);
z410=(6v,10v);

z54=(8v,4v);
z55=(8v,5v);
z56=(8v,6v);
z57=(8v,7v);
z58=(8v,8v);
z59=(8v,9v);
z510=(8v,10v);

z111=(0v,11v);
z211=(2v,11v);
z311=(4v,11v);
z411=(6v,11v);
z511=(8v,11v);

pickup pencircle scaled 0.4pt;
draw(z13--z111);
draw(z23--z211);
draw(z33--z311);
draw(z43--z411);
draw(z53--z511);
drawarrow(z14--z24);
drawarrow(z16--z26);
drawarrow(z18--z28);
drawarrow(z110--z210);
drawarrow(z25--z35);
drawarrow(z27--z37);
drawarrow(z29--z39);
drawarrow(z36--z46);
drawarrow(z38--z48);
drawarrow(z47--z57);

label.top(btex x1 etex,z111);
label.top(btex x2 etex,z211);
label.top(btex x3 etex,z311);
label.top(btex x4 etex,z411);
label.top(btex x5 etex,z511);

endfig;


beginfig(3);
v:=u*5mm;

z10=(0v,0v);
z15=(0v,5v);
z16=(0v,6v);

z20=(2v,0v);
z24=(2v,4v);
z26=(2v,6v);

z30=(4v,0v);
z33=(4v,3v);
z36=(4v,6v);

z40=(6v,0v);
z42=(6v,2v);
z46=(6v,6v);

z50=(8v,0v);
z51=(8v,1v);
z56=(8v,6v);

z60=(10v,0v);
z65=(10v,5v);
z66=(10v,6v);

z70=(12v,0v);
z74=(12v,4v);
z76=(12v,6v);

z80=(14v,0v);
z83=(14v,3v);
z86=(14v,6v);

z90=(16v,0v);
z92=(16v,2v);
z96=(16v,6v);

z100=(18v,0v);
z101=(18v,1v);
z106=(18v,6v);

z110=(20v,0v);
z116=(20v,6v);


pickup pencircle scaled 0.4pt;
draw(z10--z16);
draw(z20--z26);
draw(z30--z36);
draw(z40--z46);
draw(z50--z56);
draw(z60--z66);
draw(z70--z76);
draw(z80--z86);
draw(z90--z96);
draw(z100--z106);
draw(z110--z116);
drawarrow(z15--z65);
drawarrow(z24--z74);
drawarrow(z33--z83);
drawarrow(z42--z92);
drawarrow(z51--z101);

label.top(btex $x_0$ etex,z16);
label.top(btex $x_1$ etex,z26);
label.top(btex $x_2$ etex,z36);
label.top(btex \dots etex,z66);
label.top(btex $x_{n-2}$ etex,z106);
label.top(btex $x_{n-1}$ etex,z116);

endfig;



beginfig(4);
v:=u*5mm;

z1075=(7.5v,0v);

z10=(0v,1v);
z175=(7.5v,1v);
z115=(15v,1v);

z20=(0v,2v);
z235=(3.5v,2v);
z211=(11.5v,2v);
z215=(15v,2v);

z30=(0v,3v);
z335=(3.5v,3v);
z37=(7v,3v);
z38=(8v,3v);
z311=(11.5v,3v);
z315=(15v,3v);

z40=(0v,4v);
z415=(1.5v,4v);
z455=(5.5v,4v);
z47=(7v,4v);
z48=(8v,4v);
z495=(9.5v,4v);
z413=(13.5v,4v);
z416=(15v,4v);

z50=(0v,5v);
z515=(1.5v,5v);
z53=(3v,5v);
z54=(4v,5v);
z555=(5.5v,5v);
z57=(7v,5v);
z58=(8v,5v);
z595=(9.5v,5v);
z511=(11v,5v);
z512=(12v,5v);
z513=(13.5v,5v);
z516=(15v,5v);

z60=(0v,6v);
z61=(1v,6v);
z62=(2v,6v);
z63=(3v,6v);
z64=(4v,6v);
z65=(5v,6v);
z66=(6v,6v);
z67=(7v,6v);
z68=(8v,6v);
z69=(9v,6v);
z610=(10v,6v);
z611=(11v,6v);
z612=(12v,6v);
z613=(13v,6v);
z614=(14v,6v);
z615=(15v,6v);

z71=(1v,7v);
z72=(2v,7v);
z75=(5v,7v);
z76=(6v,7v);
z79=(9v,7v);
z710=(10v,7v);
z713=(13v,7v);
z714=(14v,7v);




pickup pencircle scaled 0.4pt;
draw(z10--z115--z215--z20--cycle);
draw(z30--z37--z47--z40--cycle);
draw(z38--z315--z416--z48--cycle);
draw(z50--z53--z63--z60--cycle);
draw(z54--z57--z67--z64--cycle);
draw(z58--z511--z611--z68--cycle);
draw(z512--z516--z615--z612--cycle);
drawarrow(z71--z61);
drawarrow(z72--z62);
drawarrow(z75--z65);
drawarrow(z76--z66);
drawarrow(z79--z69);
drawarrow(z710--z610);
drawarrow(z713--z613);
drawarrow(z714--z614);
drawarrow(z515--z415);
drawarrow(z555--z455);
drawarrow(z595--z495);
drawarrow(z513--z413);
drawarrow(z335--z235);
drawarrow(z311--z211);
drawarrow(z175--z1075);

endfig;


beginfig(5);
v:=u*5mm;

z075=(7.5v,8v);

z10=(0v,7v);
z175=(7.5v,7v);
z115=(15v,7v);

z20=(0v,6v);
z235=(3.5v,6v);
z211=(11.5v,6v);
z215=(15v,6v);

z30=(0v,5v);
z335=(3.5v,5v);
z37=(7v,5v);
z38=(8v,5v);
z311=(11.5v,5v);
z315=(15v,5v);

z40=(0v,4v);
z415=(1.5v,4v);
z455=(5.5v,4v);
z47=(7v,4v);
z48=(8v,4v);
z495=(9.5v,4v);
z413=(13.5v,4v);
z416=(15v,4v);

z50=(0v,3v);
z515=(1.5v,3v);
z53=(3v,3v);
z54=(4v,3v);
z555=(5.5v,3v);
z57=(7v,3v);
z58=(8v,3v);
z595=(9.5v,3v);
z511=(11v,3v);
z512=(12v,3v);
z513=(13.5v,3v);
z516=(15v,3v);

z60=(0v,2v);
z61=(1v,2v);
z62=(2v,2v);
z63=(3v,2v);
z64=(4v,2v);
z65=(5v,2v);
z66=(6v,2v);
z67=(7v,2v);
z68=(8v,2v);
z69=(9v,2v);
z610=(10v,2v);
z611=(11v,2v);
z612=(12v,2v);
z613=(13v,2v);
z614=(14v,2v);
z615=(15v,2v);


pickup pencircle scaled 0.4pt;
draw(z10--z115--z215--z20--cycle);
draw(z30--z37--z47--z40--cycle);
draw(z38--z315--z416--z48--cycle);
draw(z50--z53--z63--z60--cycle);
draw(z54--z57--z67--z64--cycle);
draw(z58--z511--z611--z68--cycle);
draw(z512--z516--z615--z612--cycle);
drawarrow(z075--z175);
drawarrow(z415--z515);
drawarrow(z455--z555);
drawarrow(z495--z595);
drawarrow(z413--z513);
drawarrow(z235--z335);
drawarrow(z211--z311);

label.llft(btex $n$ etex,z075);
label.bot(btex $S_n$ etex,z175);
label.bot(btex $S_{n\over 2}$ etex,z335);
label.bot(btex $S_{n\over 2}$ etex,z311);
label.bot(btex $S_{n\over 4}$ etex,z515);
label.bot(btex $S_{n\over 4}$ etex,z555);
label.bot(btex $S_{n\over 4}$ etex,z595);
label.bot(btex $S_{n\over 4}$ etex,z513);

endfig;



beginfig(6);
v:=u*5mm;

z1075=(7.5v,0v);

z10=(0v,1v);
z175=(7.5v,1v);
z115=(15v,1v);

z20=(0v,2v);
z235=(3.5v,2v);
z211=(11.5v,2v);
z215=(15v,2v);

z30=(0v,3v);
z335=(3.5v,3v);
z37=(7v,3v);
z38=(8v,3v);
z311=(11.5v,3v);
z315=(15v,3v);

z40=(0v,4v);
z415=(1.5v,4v);
z455=(5.5v,4v);
z47=(7v,4v);
z48=(8v,4v);
z495=(9.5v,4v);
z413=(13.5v,4v);
z416=(15v,4v);

z50=(0v,5v);
z515=(1.5v,5v);
z53=(3v,5v);
z54=(4v,5v);
z555=(5.5v,5v);
z57=(7v,5v);
z58=(8v,5v);
z595=(9.5v,5v);
z511=(11v,5v);
z512=(12v,5v);
z513=(13.5v,5v);
z516=(15v,5v);

z60=(0v,6v);
z61=(1v,6v);
z62=(2v,6v);
z63=(3v,6v);
z64=(4v,6v);
z65=(5v,6v);
z66=(6v,6v);
z67=(7v,6v);
z68=(8v,6v);
z69=(9v,6v);
z610=(10v,6v);
z611=(11v,6v);
z612=(12v,6v);
z613=(13v,6v);
z614=(14v,6v);
z615=(15v,6v);

z71=(1v,7v);
z72=(2v,7v);
z75=(5v,7v);
z76=(6v,7v);
z79=(9v,7v);
z710=(10v,7v);
z713=(13v,7v);
z714=(14v,7v);




pickup pencircle scaled 0.4pt;
draw(z10--z115--z215--z20--cycle);
draw(z30--z37--z47--z40--cycle);
draw(z38--z315--z416--z48--cycle);
draw(z50--z53--z63--z60--cycle);
draw(z54--z57--z67--z64--cycle);
draw(z58--z511--z611--z68--cycle);
draw(z512--z516--z615--z612--cycle);
drawarrow(z71--z61);
drawarrow(z72--z62);
drawarrow(z75--z65);
drawarrow(z76--z66);
drawarrow(z79--z69);
drawarrow(z710--z610);
drawarrow(z713--z613);
drawarrow(z714--z614);
drawarrow(z515--z415);
drawarrow(z555--z455);
drawarrow(z595--z495);
drawarrow(z513--z413);
drawarrow(z335--z235);
drawarrow(z311--z211);
drawarrow(z175--z1075);

label.top(btex $M_8$ etex,z175);
label.top(btex $M_4$ etex,z335);
label.top(btex $M_4$ etex,z311);
label.top(btex $M_2$ etex,z515);
label.top(btex $M_2$ etex,z555);
label.top(btex $M_2$ etex,z595);
label.top(btex $M_2$ etex,z513);

endfig;


beginfig(7);
v:=u*7mm;

z12=(1v,2v);
z13=(1v,3v);
z16=(1v,6v);
z356=(3.5v,6v);
z40=(5v,1v);
z42=(5v,2v);
z47=(5v,6.5v);
z72=(9v,2v);
z74=(9v,4v);
z76=(9v,6v);

z100=(0.5v,0.5v);
z101=(1.5v,0.5v);

z0=whatever[z13,z356];
z1=whatever[z356,z74];
z1=z0+4v*right;
z2=whatever[z12,z72];
z2=z0+whatever*down;
z3=whatever[z12,z72];
z3=z1+whatever*down;
z4=z356+4v*right;
z5=whatever[z72,z76];
z5=whatever[z4,z1+4v*right];
z6=whatever[z40,z47];
z6=z74+4v*left;


pickup pencircle scaled 0.4pt;
draw(z16--z12--z72--z76);
draw(z13--z356--z74);
draw(z40--z47) dashed evenly;
draw(z1--z4) dashed withdots scaled 0.7;
draw(z4--z5) dashed withdots scaled 0.7;
draw(z0--z6) dashed withdots scaled 0.7;
draw(z0--z2) dashed evenly;
draw(z1--z3) dashed evenly;

draw(z100--z101) dashed withdots scaled 0.7;

pickup pencircle scaled 3pt;
drawdot(z0);
drawdot(z1);

label.bot(btex \strut 0 etex,z12);
label.bot(btex $k$ etex,z2);
label.llft(btex \strut ${n\over 2} - 1$ etex,z42);
label.bot(btex \strut $k+{n\over 2}$ etex,z3);
label.bot(btex \strut $n-1$ etex,z72);
label.rt(btex posloupnost prohozen\'a separ\'atorem etex,z101);

endfig;







end;