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An Erdős-Ko-Rado Theorem for Multisets
2011
Electronic Journal of Combinatorics
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The size and structure of the largest intersecting collection of $k$-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. ...
doi:10.37236/707
fatcat:k4dcwq6aiva3rjviwucpnmbcxy
An Erdős-Ko-Rado theorem for multisets
[article]
2011
arXiv
pre-print
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The size and structure of the largest intersecting collection of k-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. ...
arXiv:1111.4493v1
fatcat:d6pqiyz6vvbyncguarlqyx7oce
An Erdös-Ko-Rado theorem for multisets
1988
Discrete Mathematics
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vector in SC 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. ...
doi:10.1016/0012-365x(88)90172-0
fatcat:foxnpc6hxbhwpbjwh5j2lea5mq
Elementary Techniques for Erdos-Ko-Rado-like Theorems
[article]
2008
arXiv
pre-print
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The well-known 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. ...
arXiv:0808.0774v2
fatcat:hsoy3xfoqvgevgxfz2zbtjakc4
A discrete isodiametric result: the Erdős-Ko-Rado theorem for multisets
[article]
2014
arXiv
pre-print
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There are many generalizations of the 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. ...
arXiv:1212.1071v2
fatcat:wufurhu7jne4ziv3jwbt2mkyw4
A discrete isodiametric result: The Erdős–Ko–Rado theorem for multisets
2015
European journal of combinatorics (Print)
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There are many generalizations of the 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. ...
doi:10.1016/j.ejc.2015.02.023
fatcat:rozxnnj5jzaqlmqaazcx4yoa2q
Intersection theorems for multisets
[article]
2015
arXiv
pre-print
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These results include a 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. ...
arXiv:1504.06657v2
fatcat:ikbzeewhpnhbhd5wyyeaomkaa4
Erdős-Ko-Rado-type results over Jq(n, d), Hq(n, d) and their designs
1999
Discrete Mathematics
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In terms of the notion of a specific class of ranked semilattices, called regular quantum matroids, we prove the Erdiis-Kc-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. ...
doi:10.1016/s0012-365x(98)00171-x
fatcat:prb7nvgutfb4fo6dfgqtas6qpm
The Spectral Radii of Intersecting Uniform Hypergraphs
2020
Communications on Applied Mathematics and Computation
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This paper states spectral versions of the 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 ...
doi:10.1007/s42967-020-00073-7
fatcat:qizeyvoywvazpm7wzvrgqlflva
Pseudo-LYM Inequalities and AZ Identities
1997
Advances in Applied Mathematics
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We give pseudo-LYM inequalities in some posets and give a new restriction in this way 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. ...
doi:10.1006/aama.1997.0542
fatcat:yf6b32bcjjhlbfkn7g2h5knqmm
Erdős-Ko-Rado theorem and bilinear forms graphs for matrices over residue class rings
[article]
2020
arXiv
pre-print
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As a result, the 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. ...
arXiv:2002.03560v1
fatcat:765th7chwfczpf2mq2duzhpjsu
High dimensional Hoffman bound and applications in extremal combinatorics
2022
Algebraic Combinatorics
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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. ...
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. ...
doi:10.5802/alco.190
fatcat:fghev5ns45c2pahyk2a2ncqj4a
High dimensional Hoffman bound and applications in extremal combinatorics
[article]
2019
arXiv
pre-print
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As another application, we provide spectral proofs 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. ...
arXiv:1911.02297v1
fatcat:zf7lwyvnw5bldlw4zahqmy7thi
Advances on Extremal Problems in Number Theory and Combinatorics
[chapter]
2001
European Congress of Mathematics
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It implies also 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. ...
doi:10.1007/978-3-0348-8268-2_9
fatcat:kwo7jxkbxfb4xanzt2bp4kwzhe
3-Wise Exactly 1-Intersecting Families of Sets
2005
Graphs and Combinatorics
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Let g(l, t, n) be the maximal size of 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. ...
doi:10.1007/s00373-004-0592-x
fatcat:ewhee6jco5dqtdch7uk7kaigym
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