Enumeration of Certain Binary Arrays

Author

• Douglas Jackson

Publication Date

5-8-1969

Abstract

T.V. Narayana [9] and later L. Carlitz [3] have solved the following problem. Given positive integers n, r, L₁,…,L_n-1, a₁,…,a_n such that a_i ≥ r, i = 1,...,n and a_i + L_i ≥ a_i+l, i = 1,…,n-1, how many n x r matrices [a_ij] of positive integers are there which satisfy

1.) a_i1 = a_i i=1,...,n

2.) a_ij > a_i,j+1 i = 1,...,n j = 1,..., r-1

3.) a_ij + L_i ≥ a_i+1,j i=1,...,n-1 j=1,...,r.

Narayana gave a formula for the number of such matrices in terms of a determinant of binomial coefficients.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Roger Charles Entringer

Second Committee Member

Richard Clyde Metzler

Third Committee Member

Julius Rubin Blum

Fourth Committee Member

Lambert Herman Koopmans

Fifth Committee Member

Donald Ward Dubois

Language

English

Document Type

Dissertation

Recommended Citation

Jackson, Douglas. "Enumeration of Certain Binary Arrays." (1969). https://digitalrepository.unm.edu/math_etds/269