Browsing Department of Mathematics by Author "Beard, Jacob T. B., Jr."
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Infinitely Many Perfect and Unitary Perfect Polynomials Over Some GF(q)
Harbin, Mickie Sue; Bullock, A.T.; Beard, Jacob T. B., Jr. (University of Texas at ArlingtonDepartment of Mathematics, 1977-05)**Please note that the full text is embargoed** ABSTRACT: The existence is shown of infinitely many non-splitting perfect polynomials over GF(2d), GF(3d), GF(5d) for each odd integer d > 1, and over GF(2d) for each (even) ... -
Matrix Fields Over the Integers Modulo m
McConnel, Robert M.; Beard, Jacob T. B., Jr. (University of Texas at ArlingtonDepartment of Mathematics, 1974-10)**Please note that the full text is embargoed** ABSTRACT: Let Zm denote the ring of integers modulo m and let [see pdf for notation] denote the complete ring of all [see pdf for notation] matrices over Zm under the usual ... -
Non-Splitting Unitary Perfect Polynomials Over GF(q)t
Harbin, Mickie Sue; Beard, Jacob T. B., Jr. (University of Texas at ArlingtonDepartment of Mathematics, 1978-10)**Please note that the full text is embargoed** ABSTRACT: It has been conjectured that there are infinitely many distinct pd-equivalence classes of non-splitting unitary perfect polynomials over GF(pd) for each prime ... -
Perfect Polynomials Over GF(q)
O'Connell, James R., Jr.; Beard, Jacob T. B., Jr.; West, Karen I. (University of Texas at ArlingtonDepartment of Mathematics, 1975-03)**Please note that the full text is embargoed** ABSTRACT: A monic polynomial [see pdf for notation] is called perfect over GF(q) if and only if the sum [see pdf for notation] of the distinct monic divisors in GF[q,x] of ... -
A Polynomial Dual of Partitions
Beard, Jacob T. B., Jr.; Dorris, Ann D. (University of Texas at ArlingtonDepartment of Mathematics, 1974-09)**Please note that the full text is embargoed** 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 ... -
Unitary Perfect Polynomials Over GF(q)
Beard, Jacob T. B., Jr. (University of Texas at ArlingtonDepartment of Mathematics, 1975-03)**Please note that the full text is embargoed** ABSTRACT: For monic polynomials A(x), B(x) e GF[q,x], call B(x) a unitary divisor of A(x) provided (B(x),A(x)/B(x)) = 1 . The polynomial A(x) is called unitary perfect over ...