Filters








46,207 Hits in 5.6 sec

An upper bound for the p-rank of a translation plane

Jennifer D Key, Kirsten Mackenzie
1991 Journal of combinatorial theory. Series A  
Let I7 be a projective translation plane of order q = pm. Let rk,(n) denote the rank of an incidence matrix for 17 over the field IF,.  ...  Then Further, the summation term here is the p-rank of the afftne geometry design x&"(p) of points and m-flats in the 2m-dimensional vector space over [F,. 0 1991 Academic Press, Inc.  ...  I~TR00ucTl0N Let I7 be a projective translation plane of order q = pm, L a translation line for 17, and R = I7= the derived affine translation plane.  ... 
doi:10.1016/0097-3165(91)90039-j fatcat:ots2cvrfgre4zk2vikwdvnkxsu

Page 3666 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
Hermitian varieties) is excluded by using the rank formula, and an upper bound for the size of a cap in these spaces is obtained. {For the entire collection see MR 97i:05004. } David G.  ...  To obtain a bound for m2(4,q), it is necessary to have a bound for m}(3,q), the size of the second largest complete cap in PG(3,q). By refining an approach due to B. Segre [Atti Accad. Naz.  ... 

A Rank Lower Bound for Cutting Planes Proofs of Ramsey's Theorem

Massimo Lauria
2016 ACM Transactions on Computation Theory  
We study the complexity of proving upper bounds for the number r(k, k).  ...  In particular we focus on the propositional proof system cutting planes; we prove that the upper bound "r(k, k) ≤ 4 k " requires cutting planes proof of high rank.  ...  In this paper we prove a rank lower bound of roughly Ω( 4 √ n). The Rank of a Cutting Planes Refutation One complexity measure for cutting planes is the "rank" of an inference.  ... 
doi:10.1145/2903266 fatcat:aikdisyslzflboe65jqgi6p4l4

Page 4777 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
This paper addresses the question of strict upper bounds in this case. The main result is a strict upper bound for g = 6 and rank greater than 3.  ...  Nonetheless, the number of points in this combinatorial geometry is bounded above just as a subset of PG(n — 1,q) is: it has at most (g” —1)/(q—1) points, with the upper bound achieved only by the entire  ... 

A Rank Lower Bound for Cutting Planes Proofs of Ramsey's Theorem [chapter]

Massimo Lauria
2013 Lecture Notes in Computer Science  
We study the complexity of proving upper bounds for the number r(k, k).  ...  In particular we focus on the propositional proof system cutting planes; we prove that the upper bound "r(k, k) ≤ 4 k " requires cutting planes proof of high rank.  ...  Acknowledgment Part of this work was done while the first author was at the Math Institute of the Czech Academy of Science, funded by the Eduard Čech Center.  ... 
doi:10.1007/978-3-642-39071-5_26 fatcat:tb624rsot5dtbi56vwgstndnku

Optimal anisotropic three-phase conducting composites: Plane problem

Andrej Cherkaev, Yuan Zhang
2011 International Journal of Solids and Structures  
The bound expands the Hashin-Shtrikman and translation bounds to multiphase structures, it is derived using a combination of translation method and additional inequalities on the fields in the materials  ...  The optimal microstructures are laminates of some rank for all regions.  ...  The obtained results allows for the upper bound determination for the G-closure of materials with conductivities k 1 = 0 < k 2 < k 3 < 1. Bounds. The problem of exact bounds has a long history.  ... 
doi:10.1016/j.ijsolstr.2011.05.024 fatcat:u26wwpbztveunhlhqshethpt5u

Page 262 of Mathematical Reviews Vol. , Issue 92a [page]

1992 Mathematical Reviews  
Vikram Jha (1-TXSA) 92a:51005 51E15 05B25 Key, Jennifer D. (1-CLEM); Mackenzie, Kirsten (1-CLEM) An upper bound for the p-rank of a translation plane. J. Combin. Theory Ser.  ...  A 56 (1991), no. 2, 297-302. Summary: “Let I be a projective translation plane of order g = p™. Let rk,(Il) denote the rank of an incidence matrix for II over the field F,. Then rky(T) <q?  ... 

Page 4148 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
For stochastic programs with recourse an easily computable upper bound is needed. Most of these bounds are derived by consid- ering various moment problems.  ...  The global rank is defined as the rank for which at least one of the integer nonnegative solutions of the Diophantine equation corresponds to a feasible integer point of the problem.  ... 

Page 7114 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
This yields an O(n*logn) bound on the Chvatal rank of P since any 0/1- polytope P; can be represented by a system of inequalities Ax < b with A € Z”, b © Z" such that the absolute value of each entry in  ...  A 104 (2003), no. 1, 201-206. Summary: “Two new relatives of the Upper Bound Theorem are established. The first is a variant of the Strong Upper Bound Theorem for even-dimensional simplicial spheres.  ... 

Scattered Spaces in Galois Geometry [article]

Michel Lavrauw
2016 arXiv   pre-print
This is a survey paper on the theory of scattered spaces in Galois geometry and its applications.  ...  The author thanks the members of the Algebra group of Sabancı University for their hospitality and the anonymous referees for their comments and suggestions.  ...  Theorem 3.3 implies the existence of a scattered plane w.r.t. a plane spread in PG(5, q), answering one of the questions from Example 3.1. 3. 3. An upper bound on the dimension of scattered spaces.  ... 
arXiv:1512.05251v2 fatcat:xhhabrelpzazvi45fjgvprcbt4

Page 9059 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
The Gauss-Bonnet theorem allows one to find suitable upper bounds for the boundary volume. An inequality for the isoperimetric defect enables the author to complete the proof.  ...  > 1, where w;, is the ratio of the width of C to the width of P for the direction perpendicular to the i-th pair of parallel facets of P. We prove three weaker inequalities.  ... 

Page 7464 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
The lower bound for |S| is derived from an upper bound for the number of t-fold nuclei of a set of points in AG(2, q).  ...  Although this lower bound is sharp for certain pairs (t,q), the paper obtains an improvement for Bruen’s lower bound by showing that |S| > (t+ 1)g —1 for (t,q) =1.  ... 

Finite geometries

A. Blokhuis, J. W. P. Hirschfeld, D. Jungnickel, J. A. Thas
2008 Designs, Codes and Cryptography  
Thas, A Lenz-Barlotti classification for finite generalized quadrangles V.D. Tonchev, Formulas for the number of STS and SQS of low 2-rank H. Van Maldeghem, Some remarks on Steiner systems 3  ...  Edel, Extensions of generalized product caps A. Gács, Some new results about directions D.G. Glynn, The invariant graphs, tournaments and codes of projective planes of even order P.  ...  One easily obtains an upper bound of q 3 − q + 1 for this 2−rank, and we conjecture that indeed this bound is the 2−rank.  ... 
doi:10.1007/s10623-007-9162-6 fatcat:yd5cqfmlrfa7zlzeifhhx7qfg4

Strengthening Chvátal-Gomory Cuts for the Stable Set Problem [chapter]

Adam N. Letchford, Francesca Marzi, Fabrizio Rossi, Stefano Smriglio
2016 Lecture Notes in Computer Science  
As a result, the overall procedure proves to be capable of yielding competitive upper bounds in reasonable computing times.  ...  The main difficulty is that upper bounds based on linear programming (LP) tend to be weak, whereas upper bounds based on semidefinite programming (SDP) take a long time to compute.  ...  Algorithm 1 Cutting plane algorithm Input: Formulation Q(C) Output: An updated formulation P, the upper bound CG-S; Parameters: niter,cutviolation,septlim, rhstlim,maxpercnz,minimprove P ← Q(C) Optimize  ... 
doi:10.1007/978-3-319-45587-7_18 fatcat:j24k6alfvngnbgu63h4ovlhpbu

Translation nets: a survey

Dirk Hachenberger, Dieter Jungnickel
1992 Discrete Mathematics  
Jungnickel, Translation nets: a survey, Discrete Mathematics 106/107 (1992) 231-242. We survey some recent results on translation nets.  ...  A natural question, which was first dealt with by Jungnickel [21] is to ask for upper bounds for the degree r of a translation net with translation group G provided that G is not elementary abelian.  ...  Let N be an (s, r)-net and N' an (s, r -1)-subnet of N. If p is a prime dividing s for which p* does not divide s, one has (6.1.1) rank,(N) -rank,,(N') 2s -r + 1.  ... 
doi:10.1016/0012-365x(92)90550-y fatcat:42bt64ilmjdfflqgkzihfygukm
« Previous Showing results 1 — 15 out of 46,207 results