ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

13. Combinatorics

1991 MS Classification: 05-XX Combinatorics Paseman, Gerhard R., Berkeley, CA USA A different approach to Hadamard’s maximum determinant problem Let n > 0 be an integer, and D_{n} a subset of non-negative integers given by the collection of all values |d| such that d is the determinant of an n-by-n 0-1 matrix. The spectrum problem asks for an alternate characterization of D_{n}, and generalizes the problem of the title. An improvement is given on a result of Clements and Lindstroem about a large value in D_{n}. It is shown that D_{n} is not always an interval of integers, suggesting the subproblem of finding the largest interval contained in D_{n}; some results in this direction are shown. One conjecture is that solving the subproblem will solve the title problem.