Vol. 60, No. 1, 1975

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ISSN: 0030-8730
Enumeration of weighted p-line arrays

Margaret Jones Hodel

Vol. 60 (1975), No. 1, 141–167
Abstract

Let Fp(n,k;q1,q2,,qp) = Fp(n,k) be defined by

         ∑  ∏p  ∑nj=1aij
Fp(n,k) =      qi      ,
i=1

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

------------------
a    a    ⋅⋅⋅  a  |
a11  a12  ⋅⋅⋅  a1n|
|21.   2.2       2.n|
| ..   ..        .. |
ap1  ap2  ⋅⋅⋅  apn|
------------------

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=1pqi = 1, formulas for Fp(n,k) and two other enumerants, which are closely related to Fp(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
Authors
Margaret Jones Hodel