Variations of a combinatorial problem on finite sets
نویسندگان
چکیده
منابع مشابه
Some combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
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Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1,±2, . . . ,±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose tw...
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Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1,±2, · · · ,±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose tw...
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Let M be a set and F a family of its subsets. F is said by E. W. MILLER [5] to possess property B if there exists a subset K of M so that no set of the family F is contained either in K or in K (K is the complement of K in M) . HAJNAL and 1 [2] recently published a paper on the property B and its generalisations . One of the unsolved problems we state asks : What is the smallest integer in (n) ...
متن کاملA Combinatorial Theorem on Systems of Sets
It is quite easy to see that (2) and (3) give best possible results. Upper estimates for n were also given in [2] if either (Alt..., An)eS(k, </, m) and /<^(m+l) or if (Alt..., An)eS(k, I, m) and l^^(m+k), but the results in these cases are not best possible. Other results of this kind have been established in [3] and [4] which settle certain conjectures made in [2]. In this note we establish t...
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ژورنال
عنوان ژورنال: Elemente der Mathematik
سال: 2007
ISSN: 0013-6018
DOI: 10.4171/em/55