Prepletogram sestoji iz dveh dvojiških dreves s korenom z enakim številom listov in s popolnim prirejanjem med listi. V članku dokažemo, da sta obe polovici naključnega prepletograma v bistvu videti ...kot dve neodvisno izbrani naključni dvojiški drevesi. To dejstvo uporabimo, da dokažemo več rezultatov o obliki naključnih prepletogramov, vključno z izrekom o številu češenj in splošneje pojavitev poddreves, število avtomorfizmov in višina. Za vsako od teh objektov poiščemo limitne verjetnosti in porazdelitve. Na koncu proučujemo še število prirejenih češenj, kjer tudi poiščemo limitno porazdelitev.
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