Monomial Flocks and Herds Containing a Monomial Oval
نویسندگان
چکیده
منابع مشابه
Monomial Flocks and Herds Containing a Monomial Oval
Let F be a flock of the quadratic cone Q: X 2=X1X3 , in PG(3, q), q even, and let 6t : X0 =xt X1 + t X2 +zt X3 , t # Fq , be the q planes defining the flock F. A flock is equivalent to a herd of ovals in PG(2, q), q even, and to a flock generalized quadrangle of order (q, q). We show that if the herd contains a monomial oval, this oval is the Segre oval. This implies a result on the existence o...
متن کاملOn Monomial Flocks
We study monomial flocks of quadratic cones of PG(3, q), with emphasis on the case where the flock is semifield, providing some nonexistence and some uniqueness results. In addition, we give a computer-free proof of the existence of the sporadic semifield flock of the quadratic cone of PG(3, 35) (and hence of the sporadic translation ovoid of Q(4, 35)), and relate that flock to the sporadic sim...
متن کاملMonomial Ideals
Monomial ideals form an important link between commutative algebra and combinatorics. In this chapter, we demonstrate how to implement algorithms in Macaulay 2 for studying and using monomial ideals. We illustrate these methods with examples from combinatorics, integer programming, and algebraic geometry.
متن کاملMonomial Resolutions
Let M be a monomial ideal in the polynomial ring S = k[x1, . . . , xn] over a field k. We are interested in the problem, first posed by Kaplansky in the early 1960’s, of finding a minimal free resolution of S/M over S. The difficulty of this problem is reflected in the fact that the homology of arbitrary simplicial complexes can be encoded (via the Stanley-Reisner correspondence [BH,Ho,St]) int...
متن کاملMonomial Testing and Applications
In this paper, we devise two algorithms for the problem of testing q-monomials of degree k in any multivariate polynomial represented by a circuit, regardless of the primality of q. One is an O(2) time randomized algorithm. The other is an O(12.8) time deterministic algorithm for the same q-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1998
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2855