5 problems

Let $\mathrm{PG}(2,q)$ be the Desarguesian projective plane of order $q$, and let $\mathrm{Sp}(k,q)$ be the set of cardinalities of point sets avoiding $k$-secants. Complete-spectr…

Let $\Pi_q$ be a finite projective plane of order $q$, let $T_r(\Pi_q)$ denote the maximum percolation time among percolating sets at infection rate $r$, and let $r_1$ and $r_2$ be…

Let $\Pi_q$ be a finite projective plane of order $q$, let $r$ be the infection rate, and let $t_r(A)$ denote the percolation time of a percolating set $A$. Two-round minimal perco…

Let $(P,L)$ be a linear space with $d=\#P$, and let $A$ be its associated ring. Set $n$ and $m$ to be the minimum and maximum, respectively, size of a line in $L$. Suppose…

Let $q$ be the order of the finite projective plane, and let $f(n)$ denote the minimum number of lines whose odd-intersection point set has size $n$. Conjecture. … The paper has es…