A Polynomial Dual of Partitions

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A Polynomial Dual of Partitions

Show simple item record Beard, Jacob T. B., Jr. Dorris, Ann D. 2010-05-26T15:54:31Z 2010-05-26T15:54:31Z 1974-09
dc.description.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. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;15
dc.subject D-invariant transformation en
dc.subject Polynomials en
dc.subject Multi-graph en
dc.subject Cartesian product en
dc.subject.lcsh Mathematics Research en
dc.title A Polynomial Dual of Partitions en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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