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Lethbridge Number Theory and Combinatorics Seminar
Date: February 29, 2016
Time: 12:00-12:50pm
Lecturer(s): Robert Craigen (University of Manitoba)
Location: University of Lethbridge
Topic: Survey of Negacyclic Weighing Matrices
Description (in plain text format):
A square or rectangular matrix is circulant if every row after the first is a right circular shift of its predecessor. Negacyclic matrices are defined the same way except that the first entry of each row is negated after circulating the preceding row. A partial Hadamard matrix is a rectangular kxn (1,-1)-matrix M satisfying MM^T = nI.
In the summer of 2013 I hired four sharp undergraduate students to tackle a problem about circulant partial Hadamard matrices. The question of existence of certain negacyclic weighing matrices kept coming up, so we devoted some energy to exploring this largely uncultivated territory. In the end we produced, apparently for the first time, a fairly comprehensive survey of these objects, their structure, why certain classes exist and others cannot. The flavour of the existence questions for this class of weighing matrices is decidedly different from that of group-developed form, even though much of the theory is the same.
We discuss some situations in which negacyclic weighing matrices naturally appear, and conclude with some tantalizing new open questions arising from the work.
Other Information:
Location: C630 University Hall
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | uleth.ca/artsci/math-computer-science
