Date of Award
5-2008
Document Type
Thesis
Degree Name
Master of Science (MS)
Legacy Department
Mathematical Science
Committee Chair/Advisor
Calkin, Neil J
Committee Member
Matthews , Gretchen L
Committee Member
Gallagher , Colin M
Abstract
Let M(n,s) be the number of nxn matrices with binary entries, row and column sum s, and whose rows are in lexicographical order. Let S(n) be the number of nxn matrices with entries from {0,1,2}, symmetric, with trace 0, and row sum 2. (The sequence S(n) appears as A002137 in N.J.A. Sloane's Online Encyclopedia of Integer Sequences.)
We give two proofs to show that M(n,2)=S(n). First, we show they satisfy the same recurrence. Second, we give an explicit bijection between the two sets. We also show that the bijection maintains the cycle structure of our matrices.
Let M_s(n,2) be the set of symmetric matrices in M(n,2). We will show M_s(n,2) satisfies the Fibonacci sequence.
Recommended Citation
Janoski, Janine, "ORDERED MATRICES OF PRESCRIBED ROW AND COLUMN SUM" (2008). All Theses. 317.
https://tigerprints.clemson.edu/all_theses/317