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Év szerint | Hónap szerint | Ugrás a hónaphoz | |
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Eszter K. Horváth and Zoltán Németh: The combinatorics of lattices and posets |
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Szerda, 23. November 2022, 10:10 - 11:40
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This is a joint work with Delbrin Ahmed (first part) and Andreja Tepavcevic (second part). In the first part of the talk, the number of subuniverses of semilattices defined by arbitrary and special kinds of trees will be given via combinatorial considerations. Using a result of Freese and Nation, we give a formula for the number of congruences of semilattices defined by arbitrary and special kinds of trees, as well as some interesting properties of the congruence lattice of a semilattice corresponding to a tree. Using the number of subuniverses and the number of congruences, we will give a formula for the number of weak congruences of semilattices defined by a binary tree. Some special cases will be discussed. The solution of two apparently nontrivial recurrences will be presented. In the second part of the talk, we determine the two greatest numbers of weak congruences of lattices. The number of weak congruences of some special lattices, such as lanterns (on a chain) and chandeliers, will be deduced via combinatorial considerations. The lecture will be in the Riesz lecture room. |
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