Time: 09h00 - 10h00, Tuesday 23.07.2024

Location: Room 617, building A6, Institute of Mathematics (18 Hoang Quoc Viet, Cau Giay, Hanoi)

Abstract: We examine a connection between a partially ordered set (poset) and its incidence matrix called a poset matrix, especially how partial orders of posets are encoded in matrix form. This talk presents a comprehensive study of these matrices and their relevance in solving the long-standing combinatorial challenge of counting non-isomorphic posets, posed by Birkhoff in 1948. We introduce a technique for indexing and constructing poset matrices derived from the binary Pascal matrix using the concept of binary representation matrices. New insights into the structural properties of these matrices are also provided. This idea may provide a promising route to address fundamental questions in the field of poset theory and may also open new possibilities for practical applications.