Enumeration of weighted p-line arrays

Margaret Jones Hodel

Vol. 60 (1975), No. 1, 141–167

DOI: 10.2140/pjm.1975.60.141

Abstract

Let F_p(n,k;q₁,q₂,⋯,q_p) = F_p(n,k) be defined by

where the summation is over all p-line arrays of positive integers

subject to the following conditions:

max{aij : 1 ≦ i ≦ p}≦	min{ai,j+1 : 1 ≦ i ≦ p},		1 ≦ j ≦ n − 1,
	max{aij : 1 ≦ i ≦ p}≦ j,		1 ≦ j ≦ n,
and
	ain = k,		1 ≦ i ≦ p.

Assuming ∏ _i=1^pq_i = 1, formulas for F_p(n,k) and two other enumerants, which are closely related to F_p(n,k), are obtained in this paper. These three functions generalize enumerants which Carlitz has determined.

Mathematical Subject Classification 2000

Primary: 05A15

Milestones

Received: 11 December 1973

Published: 1 September 1975