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Nests and nest accessories
Jeremy M. Dover
The theory of finite translation planes is intimately tied to the theory of spreads of PG(3,q), where a spread is a partition of PG(3,q) into pairwise disjoint lines. A tra…
Untouchable sets of size in
Jeremy M. Dover
An untouchable set in a projective plane is a set of points such that no line of the plane meets the set in exactly one point. Recently, Héger and Nagy (Avoiding Secants of Given S…
On the minimum blocking semioval in PG(2,11)
Jeremy M. Dover
A blocking semioval is a set of points in a projective plane that is both a blocking set (i.e., every line meets the set, but the set contains no line) and a semioval (i.e., there…
Computational Enumeration of André Planes
Jeremy M. Dover
In this paper, we address computational questions surrounding the enumeration of non-isomorphic André planes for any prime power order. We are particularly focused on providing a c…
A genealogy of the translation planes of order 25
Jeremy M. Dover
In 1992 Czerwinski and Oakden (The translation planes of order 25, J. Combin. Theory Ser. A, 59:193-217, 1992) provided an exhaustive list of all spreads of and thus of a…
Repetition in Colored Sequences of Balls
Jeremy M. Dover
In responding to a question on Math Stackexchange, the author formulated the problem of determining the number of strings of balls colored in most colors with a number of r…
A Search for Spreads of Hermitian Unitals
Jeremy M. Dover
A spread of a Hermitian unital in PG(2,q^2) is a set of q^2+q+1 pairwise disjoint blocks that partition the points of the unital. In this paper, we discuss the results of an exhaus…
Some Notes on Pairs in Binary Strings
Jeremy M. Dover
Seth (Mathematics Stack Exchange, http://math.stackexchange.com/q/1812699) posed a problem that is equivalent to the following: how many binary strings of length n have exactly k p…
On Two OEIS Conjectures
Jeremy M. Dover
Stephan (Prove or Disprove 100 Conjectures from the OES, arXiv:math/0409509v4 [math.CO])enumerates a number of conjectures regarding integer sequences contained in Sloane's On-line…