10 papers
A preliminary result for generalized intersecting families
Brian Chan
Intersecting families and blocking sets feature prominently in extremal combinatorics. We examine the following generalization of an intersecting family investigated by Hajnal, Rot…
Generalizing Galvin and Jónsson's Classification to N5
Brian T. Chan
The problem of determining (up to lattice isomorphism) which lattices are sublattices of free lattices is in general an extremely difficult and an unsolved problem. A notable resul…
Locally finite sublattices of free lattices
Brian T. Chan
The problem of determining which infinite lattices are (isomorphic to) sublattices of free lattices is in general unsolved and extremely difficult. In this note, we reduce the prob…
A generalization of balanced tableaux and marriage problems with unique solutions
Brian Chan
We consider families of finite sets that we call shellable and that have been characterized by Chang and by Hirst and Hughes as being the families of sets that admit unique solutio…
Periodic P-Partitions
Brian T. Chan
In this paper, we introduce a class of -partitions that we call periodic -partitions, then prove that such -partitions satisfy a homogeneous first-order mat…
Potential Methods for Extending Galvin and Jónsson's Characterization of Distributive Sublattices of Free Lattices
Brian T. Chan
In 1959, F.Galvin and B.Jonsson characterized distributive sublattices of free lattices in their paper. In this paper, I will create new proofs to a portion of Galvin and Jónsson's…
A Sufficient Condition for Jónsson's Conjecture and its Relationship with Finite Semidistributive lattices
Brian T. Chan
This article is part of my upcoming masters thesis which investigates the following open problem from the book, Free Lattices, by R.Freese, J.Jezek, and J.B. Nation published in 19…
A Variation of Galvin and Jónsson's approach to Sublattices of Free Lattices
Brian T. Chan
This article is part of my upcoming masters thesis which investigates the following open problem from the book, Free Lattices, by R.Freese, J.Jezek, and J.B. Nation published in 19…
A Simple Sufficient Condition for a Finitely Generated Lattice to not be Embeddable in a Free Lattice
Brian T. Chan
This article is part of my upcoming masters thesis which investigates the following open problem from the book, Free Lattices, by R.Freese, J.Jezek, and J.B. Nation published in 19…
Congruence Lattices of Certain Finite Algebras with Three Commutative Binary Operations
Brian T. Chan
A partial algebra construction of Grätzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to…