2010/12/25 by Cinzia Bisi, Bisi, Cinzia, Giampiero Chiaselotti +1
Computer Science · Mathematics · #05D05 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Optimization and Variational Analysis #cs.DM #cs.FL #math.CO #msc:05D05
paper · pdf · doi:10.48550/arxiv.1012.5486
22 pages
arxiv created 2010/12/25 · openalex publication_date 2010/12/25 · arxiv updated 2010/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce the notion of \it core for two specific classes of boolean maps on finite involution posets (which are a generalization of the boolean lattices) and we prove some extension results for such families of boolean maps. Through the properties of the core, we provide a complete characterization of such maps. The main purpose of such abstract results is their application to the study of the compatibility of a particular class of systems of linear inequalities related to a conjecture of Manickam, Miklös and Singhi (\citeManSin88, \citeManMik87), still unsolved and that can be considered dual to the theorem of Erdös-Ko-Rado \citeerd-ko-rad.