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arXiv · 1505.03256

Notes on use of generalized entropies in counting

Alexey E. Rastegin
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Abstract

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 $\alpha$-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 $k$-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.

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Alexey E. Rastegin. 2015-05-13. Notes on use of generalized entropies in counting. https://doi.org/10.1007/s00373-016-1731-x

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