Faithfulness in maniplexes

Cunningham, Gabe (avtor), Mochán, Elías (avtor), Montero, Antonio (avtor), Potočnik, Primož (avtor), Toledo, Micael (avtor)

Maniplexes generalize the flag graphs of maps and polytopes, and they have enabled the use of new techniques for constructing and analyzing polytopes. Each maniplex gives rise to a natural ranked poset of the faces and their incidence, but it is not always possible to recreate the maniplex from the poset. The first possible problem is that the mapping from flags of the maniplex to maximal chains of the poset may not be injective; in this case we say that the maniplex is unfaithful. The second is that the resulting poset may not be thin (meaning that some sections of rank 1 may have more than two proper faces), in which case the flag graph of the poset is not a maniplex. In this paper we describe a theory of faithfulness in maniplexes, laying the groundwork for future study in this area. We also classify the unfaithful maps (3-maniplexes) with at most two flag orbits, and we prove that the mix of two polytopes is a faithful maniplex that is thin if the polytopes are orientable.

• Jezik: Angleški jezik
• Ključne besede: maniplexes, polytopes, faithfullness
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: 29 str.
• Številčenje: Vol. 64, iss. 2, art. 23
• PID: 20.500.12556/RUL-185667
• UDK: 519.17:514
• ISSN pri članku: 0925-9899
• DOI: 10.1007/s10801-026-01559-y
• COBISS.SI-ID: 287929859
• Datum objave v RUL: 17.08.2026

Gradivo je del revije

• Naslov: Journal of algebraic combinatorics
• Skrajšan naslov: J. algebr. comb.
• Založnik: Springer Nature
• ISSN: 0925-9899
• COBISS.SI-ID: 2713689

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.