Annali di Matematica Pura ed Applicata

, Volume 106, Issue 1, pp 329–351

# Enumeration of weighted rectangular arrays

• Margaret J. Hodel
Article

## Summary

Let Ip(n, k; q1, q2, ..., qp)=Ip(n, k) be defined by
$$I_v (n,k) = \sum {\prod\limits_{i = 1}^v {q_i^{j\mathop = \limits^{\mathop \sum \limits^n a_{ij} } 1} } }$$
, where the summation is over all p-line arrays of positive integers {aij:1≤i≤p, 1≤j≤n} subject to the following conditions:
$$\begin{array}{*{20}c} {\max \left\{ {a_{ij} :1 \leqslant i \leqslant p} \right\} \leqslant \min \left\{ {a_{i,j + 1} :1 \leqslant i \leqslant p} \right\}, 1 \leqslant j \leqslant n - 1,} \\ {\max \left\{ {a_{ij} :1 \leqslant i \leqslant p} \right\} \leqslant j, 1 \leqslant j \leqslant n,} \\ {a_{i + 1,j} \leqslant a_{ij} , 1 \leqslant i \leqslant p - 1, 1 \leqslant j \leqslant n,} \\ \end{array}$$
and
$$a_{1j} = a_{2j} = ... = a_{pj} for k values of j, 1 \leqslant j \leqslant n$$
. Assuming$$\prod\limits_{i = 1}^p {q_i = 1}$$, formulas for Iv(n, k) and another closely related enumerant are determined in this paper. These two functions generalize enumerants which Carlitz has obtained.

## Keywords

Positive Integer Rectangular Array Related Enumerant
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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