#### Date of Award

5-2008

#### Document Type

Thesis

#### Degree Name

Master of Science (MS)

#### Legacy Department

Mathematical Science

#### 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