A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
An Erdős-Ko-Rado Theorem for Multisets

2011
*
Electronic Journal of Combinatorics
*

The size and structure of the largest intersecting collection of $k$-

doi:10.37236/707
fatcat:k4dcwq6aiva3rjviwucpnmbcxy
*multisets**for*$m \leq k$ is also given. ... We prove that*for*$m \geq k+1$, the size of the largest such collection is $\binom{m+k-2}{k-1}$ and that when $m > k+1$, only a collection of all the $k$-*multisets*containing a fixed element will attain ... Acknowledgment We are grateful*for*the helpful comments of the anonymous referee, particularly those concerning*Theorem*1.3 which greatly simplified the proof. ...##
###
An Erdős-Ko-Rado theorem for multisets
[article]

2011
*
arXiv
*
pre-print

The size and structure of the largest intersecting collection of k-

arXiv:1111.4493v1
fatcat:d6pqiyz6vvbyncguarlqyx7oce
*multisets**for*m ≤ k is also given. ... We prove that*for*m ≥ k+1, the size of the largest such collection is m+k-2k-1 and that when m > k+1, only a collection of all the k-*multisets*containing a fixed element will attain this bound. ... Acknowledgment We are grateful*for*the helpful comments of the anonymous referee, particularly those concerning*Theorem*1.3 which greatly simplified the proof. ...##
###
An Erdös-Ko-Rado theorem for multisets

1988
*
Discrete Mathematics
*

vector in SC

doi:10.1016/0012-365x(88)90172-0
fatcat:foxnpc6hxbhwpbjwh5j2lea5mq
*An*Erdiis-*Ko*-*Rado*rAeorem*for**multisets*&$. are in 9i U l l l U ! ... In looking*for*extensions of the Erdiis-*Ko*-*Rado**theorem*to*multisets*, we observe that we can extend the concept of intersection in more than one way. ...##
###
Elementary Techniques for Erdos-Ko-Rado-like Theorems
[article]

2008
*
arXiv
*
pre-print

The well-known

arXiv:0808.0774v2
fatcat:hsoy3xfoqvgevgxfz2zbtjakc4
*Erdos*-*Ko*-*Rado**Theorem*states that if F is a family of k-element subsets of 1,2,... ... We present elementary methods*for*deriving generalizations of the*Erdos*-*Ko*-*Rado**Theorem*on several classes of combinatorial objects. We also extend our results to systems under Hamming intersection. ... Anant Godbole*for*his supervision at the 2008 East Tennessee State University REU. This work was supported by NSF grant 0552730. ...##
###
A discrete isodiametric result: the Erdős-Ko-Rado theorem for multisets
[article]

2014
*
arXiv
*
pre-print

There are many generalizations of the

arXiv:1212.1071v2
fatcat:wufurhu7jne4ziv3jwbt2mkyw4
*Erdős*-*Ko*-*Rado**theorem*. ... We give new results (and problems) concerning families of t-intersecting k-element*multisets*of*an*n-set and point out connections to coding theory and classical geometry. ...*Erdős*-*Ko*-*Rado*type*theorems*Let us call a set system F intersecting if |F 1 ∩ F 2 | ≥ 1*for*all F 1 , F 2 ∈ F. ...##
###
A discrete isodiametric result: The Erdős–Ko–Rado theorem for multisets

2015
*
European journal of combinatorics (Print)
*

There are many generalizations of the

doi:10.1016/j.ejc.2015.02.023
fatcat:rozxnnj5jzaqlmqaazcx4yoa2q
*Erdős*-*Ko*-*Rado**theorem*. ... We give new results (and problems) concerning families of t-intersecting k-element*multisets*of*an*n-set and point out connections to coding theory and classical geometry. ...*Erdős*-*Ko*-*Rado*type*theorems*Let us call a set system F intersecting if |F 1 ∩ F 2 | ≥ 1*for*all F 1 , F 2 ∈ F. ...##
###
Intersection theorems for multisets
[article]

2015
*
arXiv
*
pre-print

These results include a

arXiv:1504.06657v2
fatcat:ikbzeewhpnhbhd5wyyeaomkaa4
*multiset*version of the Hilton-Milner*theorem*and a*theorem*giving the size and structure of the largest t-intersecting family of k-*multisets*of*an*m-set when m ≤ 2k-t. ... We use graph homomorphisms and existing*theorems**for*intersecting and t-intersecting k-set systems to prove new results*for*intersecting and t-intersecting families of k-*multisets*. ... The second author was supported by*an*NSERC doctoral scholarship. We would like to thank Zoltan Füredi*for*bringing reference [7] to our attention. ...##
###
Erdős-Ko-Rado-type results over Jq(n, d), Hq(n, d) and their designs

1999
*
Discrete Mathematics
*

In terms of the notion of a specific class of ranked semilattices, called regular quantum matroids, we prove the Erdiis-Kc-

doi:10.1016/s0012-365x(98)00171-x
fatcat:prb7nvgutfb4fo6dfgqtas6qpm
*Rado*-type results in a unified way*for*the association schemes J,(n,d) of vector ... Huang*for*introducing him to the Erdiis-*Ko*-*Rado*type results and*for*pointing out the arguments used in [6] . The author would also like to thank both referees*for*their comments. ... On the other hand,*an*extension of*Erdos*-K+*Rado**theorem*still holds if F is replaced by a collection of blocks of classical t-(n, k, A) designs. ...##
###
The Spectral Radii of Intersecting Uniform Hypergraphs

2020
*
Communications on Applied Mathematics and Computation
*

This paper states spectral versions of the

doi:10.1007/s42967-020-00073-7
fatcat:qizeyvoywvazpm7wzvrgqlflva
*Erdős*-*Ko*-*Rado**theorem*: let G be*an*intersecting k-uniform hypergraph on n vertices with n ⩾ 2k. ... The celebrated*Erdős*-*Ko*-*Rado**theorem*states that given n ⩾ 2k, every intersecting k-uniform hypergraph G on n vertices has at most n − 1 k − 1 edges. ... Acknowledgements The authors would like to thank the anonymous referees*for*their careful reading and providing helpful suggestions and comments on*an*earlier version of this paper, which lead to a great ...##
###
Pseudo-LYM Inequalities and AZ Identities

1997
*
Advances in Applied Mathematics
*

We give pseudo-LYM inequalities in some posets and give a new restriction in this way

doi:10.1006/aama.1997.0542
fatcat:yf6b32bcjjhlbfkn7g2h5knqmm
*for*their antichains. Typically these posets fail the LYM inequality and some of them are known not to be Sperner. ...*Erdős*, Seress, and Székely proved*an**Erdős*-*Ko*-*Rado**theorem**for*the chain poset ( [10] ). ... Observe that the number of choices*for*the coarser partition is exactly N (γ). 2 Observe that*Theorem*2.2 implies*Theorem*2.1. ...##
###
Erdős-Ko-Rado theorem and bilinear forms graphs for matrices over residue class rings
[article]

2020
*
arXiv
*
pre-print

As a result, the

arXiv:2002.03560v1
fatcat:765th7chwfczpf2mq2duzhpjsu
*Erdős*-*Ko*-*Rado**theorem**for*Z_h^m× n is obtained. ... The results on*Erdős*-*Ko*-*Rado**theorem*have inspired much research [6, 8, 17] . Let 1 ≤ r ≤ m ≤ n. ... As a result, the*Erdős*-*Ko*-*Rado**theorem**for*Z m×n h is obtained. Suppose that α i ≥ s i*for*each i ∈ I, and 0 ≤ α j < s j*for*each j ∈ [t] \ I. ...##
###
High dimensional Hoffman bound and applications in extremal combinatorics

2022
*
Algebraic Combinatorics
*

One powerful method

doi:10.5802/alco.190
fatcat:fghev5ns45c2pahyk2a2ncqj4a
*for*upper-bounding the largest independent set in a graph is the Hoffman bound, which gives*an*upper bound on the largest independent set of a graph in terms of its eigenvalues. ... The n-th tensor power of a graph with vertex set V is the graph on the vertex set V n , where two vertices are connected by*an*edge if they are connected in each coordinate. ... The authors are grateful to Ehud Friedgut, Gil Kalai, Guy Kindler, and Dor Minzer*for*valuable discussions. We thank the reviewers*for*several helpful comments and suggestions. ...##
###
High dimensional Hoffman bound and applications in extremal combinatorics
[article]

2019
*
arXiv
*
pre-print

As another application, we provide spectral proofs

arXiv:1911.02297v1
fatcat:zf7lwyvnw5bldlw4zahqmy7thi
*for*Mantel's*theorem*on triangle-free graphs and*for*Frankl-Tokushige*theorem*on k-wise intersecting families. ... One powerful method*for*upper-bounding the largest independent set in a graph is the Hoffman bound, which gives*an*upper bound on the largest independent set of a graph in terms of its eigenvalues. ... Acknowledgements The authors are grateful to Ehud Friedgut, Gil Kalai, Guy Kindler, and Dor Minzer*for*valuable discussions. Funding. ...##
###
Advances on Extremal Problems in Number Theory and Combinatorics
[chapter]

2001
*
European Congress of Mathematics
*

It implies also

doi:10.1007/978-3-0348-8268-2_9
fatcat:kwo7jxkbxfb4xanzt2bp4kwzhe
*an*Intersection*Theorem**for**multisets*of*Erdős*and Schönheim from 1969. ...*Erdős*, Seress, Székely [ErSS] and Füredi concerning*an**Erdős*-*Ko*-*Rado*-type intersection property*for*the poset of Boolean chains could also be established. ... We also present*an*extension to multi-sets and explain a connection to the (higher dimensional)*Erdős*-Moser problem. ...##
###
3-Wise Exactly 1-Intersecting Families of Sets

2005
*
Graphs and Combinatorics
*

Let g(l, t, n) be the maximal size of

doi:10.1007/s00373-004-0592-x
fatcat:ewhee6jco5dqtdch7uk7kaigym
*an*l-wise exaclty t-intersecting family that is not trivially t-intersecting. ... Let f(l,t,n) be the maximal size of a family F ⊂ 2 [n] such that any l ≥ 2 sets of F have*an*exactly t ≥ 1-element intersection. ... A simple*theorem*of*Erdős*,*Ko*and*Rado*[6] says that the maximum of |F| is 2 n−1 , if every two members of a family F ⊆ 2 [n] have a non-empty intersection. ...
« Previous

*Showing results 1 — 15 out of 72 results*