2015/05/31 by Alexey E. Rastegin
Mathematics · Physics and Astronomy · #Cardinality (data modeling) #Combinatorics #Conjecture #Discrete mathematics #Lemma (botany) #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Mathematics #Pairwise comparison #Statistical Mechanics and Entropy #Upper and lower bounds #math.CO #msc:05A20 #msc:05D40 #msc:15A15 #msc:94A17
paper · pdf · doi:10.1007/s00373-016-1731-x
published as Graphs Combin., Vol. 32, 2625-2641 (2016) · 14 pages, no figures. Except for the style, the version 3 matches the journal version. To appear in Graphs and Combinatorics
openalex publication_date 2016/08/04 · arxiv created 2016/08/08 · arxiv updated 2017/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 α-entropies of Tsallis-Havrda-Charvát 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 Brégman's theorem. A utility of the obtained bounds is explicitly exemplified.