1,720,978 research outputs found
On Af.Af* geometries
No full textThis paper is intended to be a first step towards the classification of finite flag-transitive geometries of rank 3 with affine planes and dual affine point-residues. We describe those of diameter 1. In the case of diameter > 1, we describe minimal quotients, assuming that the number of lines through two points is large enough. © 1995 Birkhäuser Verlag
C2.c geometries and generalized quadrangles of order (s-1,s+1)
No full text— A family of finite generalized quadrangles, including those of type T2*O, is characterized in this paper by a simple axiom on geometries belonging to the diagram C2.c. Adding one more axiom, a characterization of 2*O is also obtained. © 1992, Birkhäuser Verlag, Basel. All rights reserved
Semi-Boolean Steiner systems and dimensional dual hyperovals
No full textA dimensional dual hyperoval satisfying property (H) [61 in a projective space of order 2 is naturally associated with a "semi-Boolean" Steiner quadruple system. The only known examples are associated with Boolean systems. For every d > 2, we construct a new d-dimensional dual hyperoval satisfying property (H) in PG(d(d + 3)/2,2); its related semi-Boolean system is the Teirlinck one. It is universal and admits quotients in PG(n, 2), with 4d < n < d(d + 3)/2, if d greater than or equal to 6. We also prove the uniqueness of d-dimensional dual hyperovals satisfying property (H) in PG(d(d + 3)/2,2), whose related semi-Boolean systems belongs to a particular class, which includes Boolean and Teirlinck systems. Finally, we prove property (mI) [6] for them
A lower bound on the number of Semi-Boolean quadruple systems
No full textA Steiner quadruple system on points is called semi-Boolean if all of its derived triple systems on points are isomorphic to the classical one having as blocks the lines in PG. A construction of semi-Boolean Steiner quadruple systems is given, and this construction is used to prove that there are at least non-isomorphic semi-Boolean systems that are also resolvable and that admit a regular group of automorphisms
Affine attenuated spaces
No full textWe prove that a rank d geometry satisfying the “Intersection Property” and belonging to the diagram with s > 3 and d ⩾ 4 is isomorphic to an affine attenuated space (i.e., the geometry of the subspaces of a projective space not meeting a given subspace and not contained in a fixed hyperplane)
Searching for hyperbolic polynomials with span less than 4
Get PDFA monic, irreducible polynomial in one variable having integer coefficients and all real roots deserves particular interest if its roots lie in an interval of length 4 whose end-points are not integers. This follows by some pioneering studies by R. Robinson. Thanks to the crucial support of computers, a number of contributions over the decades settled the existence question for such polynomials up to degree 18. In this article, we find out that almost all of these polynomials can be recovered with algebraic operations from a few polynomials of small degree. Furthermore, a great number of the polynomials discovered by Robinson can be actually obtained as simple linear combinations of Chebyshev polynomials. As a byproduct, we found several families of hyperbolic polynomials related to Salem’s numbers
Existence of cyclic k-cycle systems of the complete graph
No full textAbstractStarting from earliest papers by Rosa we solve, directly and explicitly, the existence problem for cyclic k-cycle systems of the complete graph Kv with v≡1(mod2k), and the existence problem for cyclic k-cycle systems of the complete m-partite graph Km×k with m and k being odd. As a particular consequence, a cyclic p-cycle system of Kv with p being a prime exists for all admissible values of v but (p,v)≠(3,9). This was previously known only for p=3,5,7
The universal representation group of Huybrechts's dimensional dual hyperoval
No full textA d-dimensional dual hyperoval can be regarded as the image S = p(Σ) of a full d-dimensional projective embedding p of a dual circular space Σ. The affine expansion Exp(p) of p is a semibiplane and its universal cover is the expansion of the abstract hull p of p. In this paper we consider Huybrechts's dual hyperoval, namely p(Σ) where Σ is the dual of the affine space AG(n, 2) ⊂ PG(n, 2) and p is induced by the embedding of the line grassmannian of PG(n, 2) in PG ((n+1/2) — 1, 2). It is known that the universal cover of Exp(p) is a truncation of a Coxeter complex of type D2n and that, if Ũ is the codomain of the abstract hull p of p, then Ũ is a subgroup of the Coxeter group D of type D2n, | Ũ | = 22n -1 but Ũ is non-commutative. This information does not explain what the structure of Ũ is and how Ũ is placed inside D. These questions will be answered in this paper. © 2006, Mathematical Sciences Publishers. All rights reserved
Cyclic Hamiltonian cycle systems of the complete graph
No full textAbstractWe prove that there exists a cyclic Hamiltonian k-cycle system of the complete graph if and only if k is odd but k≠15 and pα with p prime and α>1. As a consequence we have the existence of a cyclic k-cycle system of the complete graph on km vertices for any pair (k,m) of odd integers with k as above but (k,m)≠(3,3)
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