The Experts below are selected from a list of 9 Experts worldwide ranked by ideXlab platform
Bodo Lass - One of the best experts on this subject based on the ideXlab platform.
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the Algebra of Set functions ii an enumerative analogue of hall s theorem for bipartite graphs
The Journal of Combinatorics, 2012Co-Authors: Bodo LassAbstract:Triesch (1997) [25] conjectured that Hall's classical theorem on matchings in bipartite graphs is a special case of a phenomenon of monotonicity for the number of matchings in such graphs. We prove this conjecture for all graphs with sufficiently many edges by deriving an explicit monotonic formula counting matchings in bipartite graphs. This formula follows from a general duality theory which we develop for counting matchings. Moreover, we make use of generating functions for Set functions as introduced by Lass [20], and we show how they are useful for counting matchings in bipartite graphs in many different ways.
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The Algebra of Set functions I: The product theorem and duality
European Journal of Combinatorics, 2012Co-Authors: Bodo LassAbstract:We give a comprehensive introduction to the Algebra of Set functions and its generating functions. This Algebraic tool allows us to formulate and prove a product theorem for the enumeration of functions of many different kinds, in particular injective functions, surjective functions, matchings and colourings of the vertices of a hypergraph. Moreover, we develop a general duality theory for counting functions.
Ifeoma Nnochiri - One of the best experts on this subject based on the ideXlab platform.
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On the Analytical Review of Set Theory with Applications to Classical Probability and Algebra of Boolean Logic
2020Co-Authors: C. Emmanuel Eziokwu, Ifeoma NnochiriAbstract:The Set theory has extensively been under study for centuries but it’s analysis has not systematically been presented in specific applications such as the classical probability and Algebra of Boolean logics as organized and detailed as in this paper which reviews the relevant theoretical meanings and operations of Sets in diverse approaches and as well vastly touches various anxious and Algebra of Set with examples in scientific areas. Through these examples corresponding solution were generated indicating that complicated and digital circuit problems can be easily reduced too much simplified circuit results.
C. Emmanuel Eziokwu - One of the best experts on this subject based on the ideXlab platform.
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On the Analytical Review of Set Theory with Applications to Classical Probability and Algebra of Boolean Logic
2020Co-Authors: C. Emmanuel Eziokwu, Ifeoma NnochiriAbstract:The Set theory has extensively been under study for centuries but it’s analysis has not systematically been presented in specific applications such as the classical probability and Algebra of Boolean logics as organized and detailed as in this paper which reviews the relevant theoretical meanings and operations of Sets in diverse approaches and as well vastly touches various anxious and Algebra of Set with examples in scientific areas. Through these examples corresponding solution were generated indicating that complicated and digital circuit problems can be easily reduced too much simplified circuit results.