Relevant bibliographies by topics / Kruskal-Katona theorem

Academic literature on the topic 'Kruskal-Katona theorem'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Kruskal-Katona theorem"

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Bukh, Boris. "Multidimensional Kruskal–Katona Theorem." SIAM Journal on Discrete Mathematics 26, no. 2 (January 2012): 548–54. http://dx.doi.org/10.1137/100808630.

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2

Clements, G. F. "Another generalization of the kruskal—katona theorem." Journal of Combinatorial Theory, Series A 68, no. 1 (October 1994): 239–45. http://dx.doi.org/10.1016/0097-3165(94)90104-x.

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Frohmader, Andrew. "A Kruskal–Katona type theorem for graphs." Journal of Combinatorial Theory, Series A 117, no. 1 (January 2010): 17–37. http://dx.doi.org/10.1016/j.jcta.2009.04.003.

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Clements, G. F. "Yet another generalization of the Kruskal-Katona theorem." Discrete Mathematics 184, no. 1-3 (April 1998): 61–70. http://dx.doi.org/10.1016/s0012-365x(97)00161-1.

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Ku, Cheng Yeaw, and Kok Bin Wong. "A Kruskal–Katona type theorem for integer partitions." Discrete Mathematics 313, no. 20 (October 2013): 2239–46. http://dx.doi.org/10.1016/j.disc.2013.06.001.

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London, Eran. "A new proof of the colored Kruskal—Katona theorem." Discrete Mathematics 126, no. 1-3 (March 1994): 217–23. http://dx.doi.org/10.1016/0012-365x(94)90266-6.

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Bezrukov, S., and A. Blokhuis. "A Kruskal–Katona Type Theorem for the Linear Lattice." European Journal of Combinatorics 20, no. 2 (February 1999): 123–30. http://dx.doi.org/10.1006/eujc.1998.0274.

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D'Andrea, Alessandro, and Luca De Sanctis. "The Kruskal-Katona Theorem and a Characterization of System Signatures." Journal of Applied Probability 52, no. 2 (June 2015): 508–18. http://dx.doi.org/10.1239/jap/1437658612.

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We show how to determine if a given vector can be the signature of a system on a finite number of components and, if so, exhibit such a system in terms of its structure function. The method employs combinatorial results from the theory of (finite) simplicial complexes, and provides a full characterization of signature vectors using a theorem of Kruskal (1963) and Katona (1968). We also show how the same approach can provide new combinatorial proofs of further results, e.g. that the signature vector of a system cannot have isolated zeroes. Finally, we prove that a signature with all nonzero entries must be a uniform distribution.
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D'Andrea, Alessandro, and Luca De Sanctis. "The Kruskal-Katona Theorem and a Characterization of System Signatures." Journal of Applied Probability 52, no. 02 (June 2015): 508–18. http://dx.doi.org/10.1017/s000186780001260x.

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We show how to determine if a given vector can be the signature of a system on a finite number of components and, if so, exhibit such a system in terms of its structure function. The method employs combinatorial results from the theory of (finite) simplicial complexes, and provides a full characterization of signature vectors using a theorem of Kruskal (1963) and Katona (1968). We also show how the same approach can provide new combinatorial proofs of further results, e.g. that the signature vector of a system cannot have isolated zeroes. Finally, we prove that a signature with all nonzero entries must be a uniform distribution.
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10

D'Andrea, Alessandro, and Luca De Sanctis. "The Kruskal-Katona Theorem and a Characterization of System Signatures." Journal of Applied Probability 52, no. 02 (June 2015): 508–18. http://dx.doi.org/10.1017/s0021900200012602.

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Abstract:
We show how to determine if a given vector can be the signature of a system on a finite number of components and, if so, exhibit such a system in terms of its structure function. The method employs combinatorial results from the theory of (finite) simplicial complexes, and provides a full characterization of signature vectors using a theorem of Kruskal (1963) and Katona (1968). We also show how the same approach can provide new combinatorial proofs of further results, e.g. that the signature vector of a system cannot have isolated zeroes. Finally, we prove that a signature with all nonzero entries must be a uniform distribution.
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Dissertations / Theses on the topic "Kruskal-Katona theorem"

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Ellis, Robert B. "A Kruskal-Katona theorem for cubical complexes." Thesis, Virginia Tech, 1996. http://hdl.handle.net/10919/45075.

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The optimal number of faces in cubical complexes which lie in cubes refers to the maximum number of faces that can be constructed from a certain number of faces of lower dimension, or the minimum number of faces necessary to construct a certain number of faces of higher dimension. If m is the number of faces of r in a cubical complex, and if s > r(s < r), then the maximum(minimum) number of faces of dimension s that the complex can have is m(s/r) +. (m-m(r/r))(s/r), in terms of upper and lower semipowers. The corresponding formula for simplicial complexes, proved independently by J. B. Kruskal and G. A. Katona, is m(s/r). A proof of the formula for cubical complexes is given in this paper, of which a flawed version appears in a paper by Bernt Lindstrijm. The n-tuples which satisfy the optimaiity conditions for cubical complexes which lie in cubes correspond bijectively with f-vectors of cubical complexes.
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Book chapters on the topic "Kruskal-Katona theorem"

1

Mehta, Bhavik. "Formalising the Kruskal-Katona Theorem in Lean." In Lecture Notes in Computer Science, 75–91. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16681-5_5.

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Herzog, Jürgen, and Takayuki Hibi. "Hilbert functions and the theorems of Macaulay and Kruskal–Katona." In Monomial Ideals, 97–113. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-106-6_6.

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