# Search Results

## You are looking at 1 - 3 of 3 items for :

• "polynomial ideals"
Clear All

# Balancing sets of vectors

Studia Scientiarum Mathematicarum Hungarica
Author: Gábor Hegedűs

Let n be an arbitrary integer, let p be a prime factor of n . Denote by ω 1 the p th primitive unity root,

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\omega _1 : = e^{\tfrac{{2\pi i}} {p}}$$ \end{document}
.Define ω iω 1 i for 0 ≦ ip − 1 and B ≔ {1, ω 1 , …, ω p −1 } n ⊆ ℂ n .Denote by K ( n; p ) the minimum k for which there exist vectors ν 1 , …, ν kB such that for any vector wB , there is an i , 1 ≦ ik , such that ν i · w = 0, where ν · w is the usual scalar product of ν and w .Gröbner basis methods and linear algebra proof gives the lower bound K ( n; p ) ≧ n ( p − 1).Galvin posed the following problem: Let m = m ( n ) denote the minimal integer such that there exists subsets A 1 , …, A m of {1, …, 4 n } with | A i | = 2 n for each 1 ≦ in , such that for any subset B ⊆ [4 n ] with 2 n elements there is at least one i , 1 ≦ im , with A iB having n elements. We obtain here the result m ( p ) ≧ p in the case of p > 3 primes.

Restricted access

# Algorithms for primary decomposition of modules

Studia Scientiarum Mathematicarum Hungarica
Author: Nazeran Idrees

. , Gröbner bases and primary decomposition of polynomial ideals, J. Symbolic Computations , 16 (1988), 149–167. MR 0988410 90f :68091 Zacharias G. Gröbner bases and primary

Restricted access

# An algorithm to compute a primary decomposition of modules in polynomial rings over the integers

Studia Scientiarum Mathematicarum Hungarica
Authors: Nazeran Idrees, Gerhard Pfister and Afshan Sadiq

Gianni, P., Trager, B. and Zacharias, G. , Gröbner Bases and Primary Decomposition of Polynomial Ideals, Journal of Symbolic Computation , 6 (1988), 149–167. Zacharias G. Gröbner

Open access