The N cardinality k ideals of any w-element poset (w, k variable) can be enumerated in time O(Nw). The corresponding bound for k-element subtrees of a w-element tree is O(Nw).

Let K be an infinite compact space, let C(K) be the algebra of continuous complex-valued functions of K, let F be a well-ordered chain of nonmaximal prime ideals of C(K), let IF be the smallest element of F and let MF be the unique maximal ideal of C(K) containing the elements of F . Assuming the continuum hypothesis, we show that if |C(K)/IF | = 20 , and if there exists a sequence (Gn)n≥1 of s...

In this paper, we introduce the hyper-star graph HS(n, k) as a new interconnection network, and discuss its properties such as faulttolerance, scalability, isomorphism, routing algorithm, and diameter. A hyper-star graph has merits when degree × diameter is used as a desirable quality measure of an interconnection network because it has a small degree and diameter. We also introduce a variation...

Here is the gist of the Eisenbud–Sturmfels paper Binomial ideals, Duke Math. J. 84 (1996), 1–45. The main results are that the associated primes, the primary components, and the radical of a binomial ideal in a polynomial ring are binomial if the base ring is algebraically closed. Throughout, R = k[X1, . . . , Xn], where k is a field and X1, . . . , Xn are variables over k. A monomial is an ele...

Fixed any term-ordering < on the set T(n) of terms in n variables x1, . . . , xn, we study homogeneous ideal a ⊆ P(n) of the ring of polynomials in n variables over a field k, via the associated order-ideal N (a), consisting of all the terms which are not maximal terms of elements of a and called sous-éscalier of a [7, 12, 14]. In particular we will focus our attention on the following combinat...

Space filling curves provide several advantages for indexing spatial data. We look at the Z-curve ordering and discuss three algorithms for navigating and querying k-dimensional Z-curves. In k-dimensional space, a single hyper-’Z’-shape in a recursive Z-curve forms a hypercube with 2k quadrants. The first algorithm concerns efficient checking whether a given quadrant of a local hyper-’Z’ inters...

For a CM-field K which is abelian over a totally real number field k and a prime number p, we show that the structure of the χ-component AχK of the p-component of the class group ofK is determined by Stickelberger elements (zeta values) (of fields containing K) for an odd character χ of Gal(K/k) satisfying certain conditions. This is a generalization of a theorem of Kolyvagin and Rubin. We defi...

We introduce the notions of anti fuzzy right ideal, anti fuzzy right k-ideal and intuitionistic fuzzy right k-ideal of semirings. We investigate the their properties and connections with right k-ideal, fuzzy right k-ideal, anti fuzzy right k-ideal. We characterize regular semiring through intuitionistic fuzzy right ideal. The semi regularity of semirings is characterized by intuitionistic fuzzy...

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. In this paper, we compute socle of $\cb$-bounded strongly stable ideals and determine that saturation number equigenerated ideals. We also provide explicit formulas for $\sat(I)$ Veronese type $I$. Using formula, show $\sat(I^k)$ is quasi-linear from beginning function explicitly.