A conic of the Veronese surface in PG(5, 3) is a quadrangle. If one such quadrangle is replaced with its diagonal triangle, then one obtains a point model K for Witt’s 5–(12, ...
For k > 2 and r ≥ 2, let G(k, r) denote the smallest positive integer g such that every increasing sequence of g integers {a1, a2, . . . , ag} with gaps aj+1 − aj ∈ {1, ....
We introduce a concept of so-called disjoint ordering for any collection of finite sets. It can be viewed as a generalization of a system of distinctive representatives for the s...
If t is a positive integer, then a partition of a non-negative integer n is a t−core if none of the hook numbers of the associated Ferrers-Young diagram is a multiple of t. These...
Given a tournament score sequence s1 ≥ s2 ≥ · · · ≥ sn, we prove that there exists a tournament T on vertex set {1, 2, . . . , n} such that the degree of any vertex i is ...