Antilanac
Antilanac je parcijalno uređen skup u kojem nikoja dva elementa nisu usporediva, dok u lancu vrijedi suprotno. Ako je A antilanac, onda mu je veličina |A|. Antilancima se bavi Spernerov teorem, Lubell-Yamamoto-Meshalkinova nejednakost, Mirskyev teorem, Dilworthov teorem i dr.[1]
Svaki lanac i antilanac u P imaju presjek u kojem je najviše jedan član. Zbog toga je duljina svakog lanca manja od najmanjeg broja antilanaca koji čija unija sadrži cijeli P, a veličina svakog antilanca je najviše jednaka najmanjem broju lanaca čija unija sadrži čitavi P.[1]
Izvori
- ↑ a b PMF Zagreb Arhivirana inačica izvorne stranice od 19. prosinca 2019. (Wayback Machine) Matija Bašić: Uvod u algebarsku topologiju - Parcijalno uređeni skupovi - O lancima i antilancima, 21. svibnja 2014., str. 1 (pristupljeno 19. prosinca 2019.)
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