20.500.12556/RUP-23030 Uniform equations for bipartite graphs and the center of a Terwilliger algebra The uniform property was introduced by P. Terwilliger in the context of graded posets and was later extended to connected bipartite graphs. The core of this definition involves the so called uniform equations that must be satisfied. Let Γ denote a connected bipartite graph. Fix a vertex x of Γand let T=T(x) denote the corresponding Terwilliger algebra. In this paper, we study the connections between the uniform equations and the center of T. We show that these uniform equations give rise to a certain subspace of the center of T. Changing the logical direction, we show that if a matrix of a particular form belongs to the center of T, then uniform equations are satisfified. Uniformno lastnost je prvi definiral P. Terwilliger v kontekstu gradiranih delno urejenih množic. Definicija je bila kasneje razširjena na povezane dvodelne grafe. Jedro te definicije so tako imenovane uniformne enačbe, ki morajo biti izpolnjene. Naj bo Γ povezan dvodelen graf. Fiksirajmo vozlišče x grafa Γ in naj bo T=T(x) pripadajoča Terwilligerjeva algebra. V tem članku študiramo povezave med uniformnimi enačbami in centrom algebre T. Pokažemo, da te uniformne enačbe porodijo določen podprostor centra algebre T. Pokažemo tudi, da če center algebre T vsebuje matriko ki je določene oblike, potem so uniformne enačbe izpolnjene. uniform equations center of a Terwilliger algebra bipartite graphs uniformne enačbe center Terwilligerjeve algebre dvodelni grafi true false true Angleški jezik Slovenski jezik Članek v reviji 2026-05-08 08:28:30 2026-05-08 08:28:34 2026-05-09 03:06:32 0000-00-00 00:00:00 2026 0 0 str. 30-52 Vol. 744 1 Sep. 2026 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2026-04-27 519.17 0024-3795 10.1016/j.laa.2026.04.024 277454339 RAZ_Miklavic_Stefko_2026.pdf RAZ_Miklavic_Stefko_2026.pdf 1 601CBCC924EC4698183EC42053C90A10 5b2138cd3291b85a343bbcbe923d2ba5df49c465246333044046c4078db37c67 3058c07e-4aa7-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33650 https://www.sciencedirect.com/science/article/pii/S0024379526001837 1 0db7dc56-4aa7-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33649 Inštitut Andrej Marušič 0 0 0