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6 papers · 1 filter
Independent domination in the graph defined by two consecutive levels of the -cube
Thomas Kalinowski, Uwe Leck
Fix a positive integer and consider the bipartite graph whose vertices are the -element subsets and the -element subsets of , and there is an edge be…
Efficient Calculation the Number of Partitions of the Set into Subsets Satisfying
Christian Hercher, Frank Niedermeyer
Consider the set . We are interested in the number of partitions of this set into subsets of three elements each, where the sum of two of them equals the third.…
Sizes of flat maximal antichains of subsets
Jerrold R. Griggs, Thomas Kalinowski, Uwe Leck +2
This is the second of two papers investigating for which positive integers there exists a maximal antichain of size in the Boolean lattice (the power set of $[n]:=\{1…
The saturation spectrum for antichains of subsets
Jerrold R. Griggs, Thomas Kalinowski, Uwe Leck +2
Extending a classical theorem of Sperner, we characterize the integers such that there exists a maximal antichain of size in the Boolean lattice , that is, the power s…
Minimum Weight Flat Antichains of Subsets
Jerrold R. Griggs, Sven Hartmann, Thomas Kalinowski +2
Building on classical theorems of Sperner and Kruskal-Katona, we investigate antichains in the Boolean lattice of all subsets of , where $\…
Multivariate Stirling Polynomials of the first and second kind
Alfred Schreiber
Two doubly indexed families of homogeneous and isobaric polynomials in several indeterminates are considered: the (partial) exponential Bell polynomials and a new family…