A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Sum-Free Sets and Related Sets

1998
*
Combinatorica
*

A

doi:10.1007/s004930050032
fatcat:qpcltsmstffehpmyelyqjgk26u
*set*A of integers is*sum*-*free*if A\(A+A) = ;. Cameron conjectured that the number of*sum*-*free**sets*A f1; : : : ; Ng is O(2 N=2 ). ... As a step towards this conjecture, we prove that the number of*sets*A f1; : : : ; Ng satisfying (A + A + A) \ (A + A + A + A) = ; is 2 (N+1)=2] (1 + o(1)). ... 2 =16)N*sum*-*free**sets*A f1; : : : ; Ng such that*and*Erd} os 4] proved that there are at most O 2 N=2*sum*-*free*subsets of f N=3]; : : : ; Ng. ...##
###
Parametric matroid of rough set
[article]

2012
*
arXiv
*
pre-print

Moreover, the parametric matroid of the rough

arXiv:1209.4975v1
fatcat:a4ybwhhfdnd6vdvp6gn7hsnmoe
*set*is proved to be the direct*sum*of a partition-circuit matroid*and*a*free*matroid. ... On the one hand, for a universe*and*an equivalence*relation*on the universe, a parametric*set*family is defined through the lower approximation operator. ... For a universe*and*an equivalence*relation*on the universe, the parametric matroid of the rough*set*with respect to a subset of the universe is the direct*sum*of a partitioncircuit matroid*and*a*free*matroid ...##
###
Parametric Matroid of Rough Set

2015
*
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems
*

Moreover, the parametric matroid of the rough

doi:10.1142/s0218488515500403
fatcat:vke7thleqnh33htpiczju4oxpa
*set*is proved to be the direct*sum*of a partition-circuit matroid*and*a*free*matroid. ... Let R be an equivalence*relation*on U*and*X ⊆ U . ... For a universe*and*an equivalence*relation*on the universe, the parametric matroid of the rough*set*with respect to a subset of the universe is the direct*sum*of a partitioncircuit matroid*and*a*free*matroid ...##
###
On the diagonal queens domination problem

1986
*
Journal of combinatorial theory. Series A
*

K is a diagonal dominating

doi:10.1016/0097-3165(86)90012-9
fatcat:h4wmspa2arep3a72hjaocihe54
*set*if*and*only if N -K is a midpoint-*free*, even-*sum**set*. ,, 2a, ,..., 2a,} or (2a, -1, 2a, -l,..., 2ak -l} is a midpoint-*free*, even-*sum**set*of ( l,..., n > if*and*only if ... The following elementary result simplifies the computation of midpointfree, even-*sum**sets**and*enables us to*relate*diag(n) to a well-studied, number-theoretic function. We omit the proof. ...##
###
Page 895 of Mathematical Reviews Vol. , Issue 84c
[page]

1984
*
Mathematical Reviews
*

Centrum, Amsterdam, 1971; MR 49 #4778] that if « is an infinite cardinal <2,

*and*|f(x)|<« for every x, then a*free**set*of cardinality 2*° exists. ... Two new operations on fuzzy*sets*, “drastic*sum*”*and*“drastic product”, are introduced*and*their properties*and*combinations with other operations are exhaustively classified under all such headings as ...##
###
Zero-sum free sets with small sum-set

2011
*
Mathematics of Computation
*

Let A be a zero-

doi:10.1090/s0025-5718-2011-02385-9
fatcat:7jmu6v5omrcktbhpvdyjsbmf2m
*sum**free*subset of Z n with |A| = k. We compute for k ≤ 7 the least possible size of the*set*of all subset-*sums*of A. ... If there are no zero-*sum**free**sets*of cardinality k in Z n , we*set*f n (k) = ∞. ... To check that the inequalities are satisfied, too, it suffices to verify that the resulting*set*B = {x 1 , . . . , x 5 } indeed consists of k different elements*and*is zero-*sum**free**and*that the*sum*-*set*...##
###
Page 3727 of Mathematical Reviews Vol. , Issue 99f
[page]

1999
*
Mathematical Reviews
*

Summary: “Cameron introduced a natural probability measure on the

*set*Y of*sum*-*free**sets*,*and*asked which*sets*of*sum*-*free**sets*have a positive probability of occurring in this probability measure. ... He showed that the*set*of subsets of the odd numbers has a positive probability,*and*that the*set*of subsets of any*sum*-*free**set*corresponding to a complete modular*sum*-*free**set*also has a positive probability ...##
###
Zero-sum free sequences with small sum-set
[article]

2008
*
arXiv
*
pre-print

Let A be a zero-

arXiv:0804.0313v1
fatcat:4g2b4xiesrcanfovwlyxkmr2ka
*sum**free*subset of Z_n with |A|=k. We compute for k\le 7 the least possible size of the*set*of all subset-*sums*of A. ... If there are no zero-*sum**free**sets*of cardinality k in Z n , we*set*f n (k) = ∞. ... Define f n (k) = min |Σ(B)| − 1, where B runs over all zero-*sum**free*subsets of Z n of cardinality k,*and**set*f (k) := min n f n (k). ...##
###
On Recognising Certain One Relation Presentations

1972
*
Proceedings of the American Mathematical Society
*

It follows from the Lemma that Hi is a one

doi:10.2307/2039032
fatcat:fnhs7dhubzhw5dzkehrapd4dqe
*relation*presentation if*and*only if {b2, bxbibxl, • • ■ , ¿Î_1è2AÎ_i} is a*free*generating*set*of Nx. ... This will be the case if*and*only if {0¿>2, (¡(b^bî1), • • • , 0(¿>Í-1A26Í-Í)} is a*free*generating*set*of N2. ...##
###
On recognising certain one relation presentations

1972
*
Proceedings of the American Mathematical Society
*

It follows from the Lemma that Hi is a one

doi:10.1090/s0002-9939-1972-0306333-4
fatcat:yvsxrycbzzdxvgn6gkm27kknmm
*relation*presentation if*and*only if {b2, bxbibxl, • • ■ , ¿Î_1è2AÎ_i} is a*free*generating*set*of Nx. ... This will be the case if*and*only if {0¿>2, (¡(b^bî1), • • • , 0(¿>Í-1A26Í-Í)} is a*free*generating*set*of N2. ...##
###
Logic Without Syntax
[article]

2005
*
arXiv
*
pre-print

Abstract propositions correspond to objects of the category G(Rel^L) where G is the Hyland-Tan double glueing construction, Rel is the standard category of

arXiv:math/0504065v1
fatcat:6im5w2ebuzg3dpca56sx7ys36u
*sets**and**relations*,*and*L is a*set*of literals ... We prove that the*free*binary product-*sum*category (contraction-weakening logic) over L is a full subcategory of Gl(Rel^L),*and*the*free*distributive lattice category (contraction-weakening-distribution ... THEOREM 1 CW K is the*free*binary product-*sum*category generated by the*set*K. Proof. ...##
###
Theoretical Bounds on the Size of Condensed Representations
[chapter]

2005
*
Lecture Notes in Computer Science
*

More concrete, we compute a lower bound for the size of the database in terms of the size of the l-

doi:10.1007/978-3-540-31841-5_4
fatcat:czh5atgwtvcmffyowman5754ka
*free**set*,*and*when the database size is smaller than this lower bound, we know that the*set*cannot be ... We will bound the maximal cardinality of an l-*free**set*based on the size of the database. ... In this way, we extend results of [7]*and*of [10] that*relate*the database size to the maximal length of respectively the non-derivable itemsets*and*the generalized disjunction*free**sets*. ...##
###
On Infinite Sum-free Sets of Natural Numbers

1997
*
Journal of Number Theory
*

It is shown that every k-

doi:10.1006/jnth.1997.2169
fatcat:5z5igrkz3jbw5evwxuf35eumlm
*sum*-*free**set*with upper density larger than 1Â(k+1) is a subset of a periodic k-*sum*-*free**set**and*that each k-*sum*-*free**set*with upper density larger than 2Â(k+3) is subset of a ... In particular, no k-*sum*-*free**set*has upper density larger than 1Â\ 1 (k), where \ 1 (k)=min[i: i |% k&1], as conjectured by Calkin*and*Erdo s. ... Furthermore, either of*relations*l (a+ g)+a l+1 + } } } +a k =a+ g*and*a 1 + } } } +a k =a+ g implies that a # kA which contradicts the fact that a belongs to the k-*sum*-*free**set*A. ...##
###
Maximum number of sum-free colorings in finite abelian groups
[article]

2017
*
arXiv
*
pre-print

On the contrary, if the largest

arXiv:1710.08352v1
fatcat:3grtl6mvabeebd4yqdgbpmuhr4
*sum*-*free**set*in G is not unique then A attains κ_r,G if*and*only if it is the union of two largest*sum*-*free**sets*(in case r=4)*and*the union of three ("independent") largest ...*sum*-*free**sets*(in case r=5). ... Consider the canonical correspondence*relating*B i , i ∈ [3] , to the*set*{i}. Then there are four further largest*sum*-*free**sets*contained in B 1 ∪B 2 ∪B 3 . ...##
###
Page 1686 of Mathematical Reviews Vol. , Issue 2000c
[page]

2000
*
Mathematical Reviews
*

/4) maximum

*sum*-*free**sets*. Theorem 2: The size of the smallest maximum*sum*-*free**set*is between c),/n*and*c2,/n. ... 2000c:05144 05 05D Extremal combinatorics 2000c:05144 05D05 11B75 Cameron, Peter J. (4-LNDQM; London); Erdés, Paul [Erdés, Paul'] (H-AOS; Budapest) Notes on*sum*-*free**and**related**sets*. ...
« Previous

*Showing results 1 — 15 out of 1,796,108 results*