A Polynomial Dual of Partitions

ResearchCommons/Manakin Repository

A Polynomial Dual of Partitions

Show full item record

Title: A Polynomial Dual of Partitions
Author: Beard, Jacob T. B., Jr.; Dorris, Ann D.
Abstract: Let [see pdf for notation] be a non-negative integral polynomial. The polynomial P(x) is m-graphical, and a multi-graph G a realization of P(x), provided there exists a multi-graph G containing exactly P(1) points where [see pdf for notation] of these points have degree i for [see pdf for notation]. For multi-graphs G,H having polynomials P(x), Q(x) and number-theoretic partitions (degree sequences) [see pdf for notation], the usual product P(x)Q(x) is shown to be the polynomial of the Cartesian product [see pdf for notation], thus inducing a natural product [see pdf for notation] which extends that of juxtaposing integral multiple copies of [see pdf for notation]. Skeletal results are given on synthesizing a multi-graph G via a natural Cartesian product [see pdf for notation] having the same polynomial (partition) as G. Other results include an elementary sufficient condition for arbitrary non-negative integral polynomials to be graphical.
Date: 1974-09

Files in this item

Files Size Format View Description
MathTechReport015.pdf 532.1Kb PDF View/Open PDF

This item appears in the following Collection(s)

Show full item record


My Account


About Us