1 research outputs found
Notes on use of generalized entropies in counting
We address an idea of applying generalized entropies in counting problems.
First, we consider some entropic properties that are essential for such
purposes. Using the -entropies of Tsallis-Havrda-Charv\'{a}t type, we
derive several results connected with Shearer's lemma. In particular, we derive
upper bounds on the maximum possible cardinality of a family of -subsets,
when no pairwise intersections of these subsets may coincide. Further, we
revisit the Minc conjecture. Our approach leads to a family of one-parameter
extensions of Br\'{e}gman's theorem. A utility of the obtained bounds is
explicitly exemplified.Comment: 14 pages, no figures. Except for the style, the version 3 matches the
journal version. To appear in Graphs and Combinatoric