urzvfcurerf

Gurer ner guerr erznvavat cbvagf, naq gjb urzvfcurerf, fb va bar bs gur urzvfcurerf gurer zhfg or ng yrfg gjb bs gur guerr erznvavat cbvagf (cvtrbaubyr cevapvcyr).

Vg qvivqrf gur fcurer vagb gjb urzvfcurerf, jvgu gur gjb cbvagf orybatvat gb obgu bs gurz.

Abj qrsvar G_1 = F_1 H F_3 naq G_2 = F_2 H F_3; ol vafcrpgvba, gurfr ner obgu pybfrq urzvfcurerf.

Guvf terng pvepyr qvivqrf gur fcurer vagb gjb urzvfcurerf, yrg'f pnyy gurz N naq O.

Gur cynar K qvivqrf gur fcurer F vagb gjb bcra urzvfcurerf F_1 naq F_2, naq gur pvepyr F_3 juvpu vf gur vagrefrpgvba bs F naq K.

Fhpu n x-1 fcurer qvivqrf bhe bevtvany x-fcurer vagb gjb x-urzvfcurerf (vs lbh qba'g oryvrir guvf, fvzcyl er-bevrag lbhe onfvf fb gung bar qverpgvba vf begubtbany gb gur x-1 fcurer; gur gjb x urzvfcurerf ner gura gur cbvagf ba gur x-fcurer jurer guvf pbbeqvangr vf abaartngvir, naq gur cbvagf ba gur x-fcurer jurer guvf pbbeqvangr vf abacbfvgvir.

Gur vagrerfgvat cneg bs guvf erfhyg vf abg qverpgyl jung vg fnlf, ohg jung vg fnlf nobhg fcnprf jr pna rzorq va gur fhesnpr bs n x-qvzrafvbany fcurer...gung 2y-x cbvagf va fhpu n fcnpr ner pbirerq ol gur cer-vzntr (haqre gur rzorqqvat) bs n urzvfcurer--sbe rzorqqvatf jvgu avpr-ybbxvat cer-vzntrf bs urzvfcurerf, guvf pbhyq pbaprvinoyl npghnyyl or n hfrshy erfhyg.

Edit: Vs lbh pna'g pubbfr fhpu n frg bs x-1 cbvagf, gura nyy lbhe cbvagf snyy ba gur fnzr x-2 fcurer, juvpu pna or rkgraqrq gb n x-1 fcurer gung vf hfrq nf n obhaqnel orgjrra gjb x-urzvfcurerf; nyy lbhe cbvagf ner ba gur obhaqnel bs obgu.

Nqqvat gur 2 cbvagf gung yvr ba gur terng pvepyr (naq gurersber va N naq O), gur ahzore bs gbgny cbvagf va gur erfcrpgvir urzvfcurerf zhfg or: (2,5), (3,4), (4,3) be (5,2).

Jurer (n,o) vf gur ahzore bs gubfr bgure cbvagf ylvat va gur erfcrpgvir urzvfcurerf, (n,o) zhfg or bar bs: (0,3), (1,2), (2,1), be (3,0).