arXiv subjects

David B. Chandler

Publications and source records attributed to David B. Chandler.

5 recordsLinked to original sources

arXiv2011

The sizes of the intersection of two unitals in PG$(2,q^2)$

We show that the size of the intersection of a Hermitian variety in $\PG(n,q^2)$, and any set satisfying an $r$-dimensional-subspace intersection property, is congruent to 1 modulo a power of $p$. In particular, in the case where $n=2$, if the two sets are a Hermitian unital and any other unital, the size of the intersection is congruent to 1 modulo $\sqrt q$ or modulo $\sqrt{pq}$. If the second unital is a Buekenhout-Metz unital, we show that the size is congruent to 1 modulo $q$.

math.CO↗

arXiv2010

Permutation Polynomials of Degree 6 or 7 over Finite Fields of Characteristic 2

In \cite{D1}, Dickson listed all permutation polynomials up to degree 5 over an arbitrary finite field, and all permutation polynomials of degree 6 over finite fields of odd characteristic. The classification of degree 6 permutation polynomials over finite fields of characteristic 2 was left incomplete. In this paper we complete the classification of permutation polynomials of degree 6 over finite fields of characteristic 2. In addition, all permutation polynomials of degree 7 over finite fields of characteristic 2 are classified.

math.CO↗

arXiv2008

Incidence Modules for Symplectic Spaces in Characteristic Two

We study the permutation action of a finite symplectic group of characteristic 2 on the set of subspaces of its standard module which are either totally isotropic or else complementary to totally isotropic subspaces with respect to the alternating form. A general formula is obtained for the 2-rank of the incidence matrix for the inclusion of one-dimensional subspaces in the distinguished subspaces of a fixed dimension.

math.CO↗

arXiv2006

The permutation action of finite symplectic groups of odd characteristic on their standard modules

Motivated by the incidence problems between points and flats of a symplectic polar space, we study a large class of submodules of the space of functions on the standard module of a finite symplectic group of odd characteristic. Our structure results on this class of submodules allow us to determine the $p$-ranks of the incidence matrices between points and flats of the symplectic polar space. In particular, we give an explicit formula for the $p$-rank of the generalized quadrangle ${\rm W}(3,q)$, where $q$ is an odd prime power. Combined with the earlier results of Sastry and Sin on the 2-rank of ${\rm W}(3,2^t)$, it completes the determination of the $p$-ranks of ${\rm W}(3,q)$.

math.CO↗

arXiv2003

The invariant factors of the incidence matrices of points and subspaces in PG(n,q) and AG(n,q)

We determine the Smith normal forms of the incidence matrices of points and projective (r-1)-dimensional subspaces of PG(n,q) and of the incidence matrices of points and r-dimensional affine subspaces of AG(n,q) for all n, r, and arbitrary prime power q.

math.CO↗