A tour of M-part L-Sperner families

Aydinian H, Czabarka E, Erdos PL, Szekely LA (2011)
Journal of Combinatorial Theory Series A 118(2): 702-725.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Aydinian, HaratyunUniBi; Czabarka, Eva; Erdos, Peter L.; Szekely, Laszlo A.
Abstract / Bemerkung
In this paper we investigate common generalizations of more-part and L-Sperner families. We prove a BLYM inequality for M-part L-Sperner families and obtain results regarding the homogeneity of such families of maximum size through the convex hull method. We characterize those M-part Sperner problems, where the maximum family size is the classical (n left perpendicularn/2right perpendicular). We make a conjecture on the maximum size of M-part Sperner families for the case of equal parts of size 2(l) - 1 and prove the conjecture in some special cases. We introduce the notion of k-fold M-part Sperner families, which specializes to the concept of M-part Sperner families for k = 1, and generalize some M-part Sperner results to k-fold M-part Sperner families. We also approach the M-part Sperner problem from the viewpoints of graph product and linear programming, and prove the 2-part Sperner theorem using linear programming. This paper can be used as a survey, as in addition to the new results, problems and conjectures, we provide a number of alternative proofs, discuss at length a number of generalizations of Sperner's theorem, and for the sake of completeness, we give proofs to many simple facts that we use. (C) 2010 Elsevier Inc. All rights reserved.
Stichworte
Homogeneity; Sperner theorem; Extremal set theory; Antichain; M-part Sperner family; BLYM inequality; Transversal; Convex hull method
Erscheinungsjahr
2011
Zeitschriftentitel
Journal of Combinatorial Theory Series A
Band
118
Ausgabe
2
Seite(n)
702-725
ISSN
0097-3165
Page URI
https://pub.uni-bielefeld.de/record/2003530

Zitieren

Aydinian H, Czabarka E, Erdos PL, Szekely LA. A tour of M-part L-Sperner families. Journal of Combinatorial Theory Series A. 2011;118(2):702-725.
Aydinian, H., Czabarka, E., Erdos, P. L., & Szekely, L. A. (2011). A tour of M-part L-Sperner families. Journal of Combinatorial Theory Series A, 118(2), 702-725. doi:10.1016/j.jcta.2010.09.006
Aydinian, H., Czabarka, E., Erdos, P. L., and Szekely, L. A. (2011). A tour of M-part L-Sperner families. Journal of Combinatorial Theory Series A 118, 702-725.
Aydinian, H., et al., 2011. A tour of M-part L-Sperner families. Journal of Combinatorial Theory Series A, 118(2), p 702-725.
H. Aydinian, et al., “A tour of M-part L-Sperner families”, Journal of Combinatorial Theory Series A, vol. 118, 2011, pp. 702-725.
Aydinian, H., Czabarka, E., Erdos, P.L., Szekely, L.A.: A tour of M-part L-Sperner families. Journal of Combinatorial Theory Series A. 118, 702-725 (2011).
Aydinian, Haratyun, Czabarka, Eva, Erdos, Peter L., and Szekely, Laszlo A. “A tour of M-part L-Sperner families”. Journal of Combinatorial Theory Series A 118.2 (2011): 702-725.

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