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» Some formulae for partitions into squares
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DM
2000
73views more  DM 2000»
13 years 10 months ago
Some formulae for partitions into squares
We consider the new problem of determining the number of partitions of a number into a fixed number k of squares, and find explicit formulae in the cases k = 2, 3, 4. Classificati...
Michael D. Hirschhorn
ARITH
2007
IEEE
14 years 5 months ago
Asymmetric Squaring Formulae
Abstract. We present efficient squaring formulae based on the Toom-Cook multiplication algorithm. The latter always requires at least one non-trivial constant division in the inte...
Jaewook Chung, M. Anwar Hasan
DM
1999
81views more  DM 1999»
13 years 10 months ago
Basis partitions and Rogers-Ramanujan partitions
Every partition has, for some d, a Durfee square of side d. Every partition with Durfee square of side d gives rise to a "successive rank vector" r = (r1,
Michael D. Hirschhorn
TPHOL
2007
IEEE
14 years 5 months ago
Verifying Nonlinear Real Formulas Via Sums of Squares
Techniques based on sums of squares appear promising as a general approach to the universal theory of reals with addition and multiplication, i.e. verifying Boolean combinations of...
John Harrison
ICTAI
2009
IEEE
14 years 5 months ago
Local Autarkies Searching for the Dynamic Partition of CNF Formulae
In this paper an original dynamic partition of formulae in Conjunctive Normal Form (CNF) is presented. It is based on the autarky concept first introduced by Monien and Speckenme...
Éric Grégoire, Bertrand Mazure, Lakh...