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

1991
*
Journal of combinatorial theory. Series A
*

Let I7 be

doi:10.1016/0097-3165(91)90039-j
fatcat:ots2cvrfgre4zk2vikwdvnkxsu
*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*. ...##
###
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

2016
*
ACM Transactions on Computation Theory
*

We study

doi:10.1145/2903266
fatcat:aikdisyslzflboe65jqgi6p4l4
*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. ...##
###
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]

2013
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/978-3-642-39071-5_26
fatcat:tb624rsot5dtbi56vwgstndnku
*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. ...##
###
Optimal anisotropic three-phase conducting composites: Plane problem

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. ...

##
###
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]

2016
*
arXiv
*
pre-print

This is

arXiv:1512.05251v2
fatcat:xhhabrelpzazvi45fjgvprcbt4
*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. ...##
###
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

2008
*
Designs, Codes and Cryptography
*

Thas,

doi:10.1007/s10623-007-9162-6
fatcat:yd5cqfmlrfa7zlzeifhhx7qfg4
*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*. ...##
###
Strengthening Chvátal-Gomory Cuts for the Stable Set Problem
[chapter]

2016
*
Lecture Notes in Computer Science
*

As

doi:10.1007/978-3-319-45587-7_18
fatcat:j24k6alfvngnbgu63h4ovlhpbu
*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 ...##
###
Translation nets: a survey

1992
*
Discrete Mathematics
*

Jungnickel,

doi:10.1016/0012-365x(92)90550-y
fatcat:42bt64ilmjdfflqgkzihfygukm
*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. ...
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