On the asymptotic behavior of some counting functions, II
Copyright policy )On the asymptotic behavior of some counting functions, II
Summary: The investigation of the counting function of the set of integral elements, in an algebraic number field, with factorizations of at most \(k\) different lengths gives rise to a combinatorial constant depending only on the class group of the number field and the integer~\(k\). In this paper the value of these constants, in case the class group is an elementary \(p\)-group, is estimated, and determined under additional conditions. In particular, it is proved that for elementary \(2\)-groups these constants are equivalent to constants that are investigated in extremal graph theory. Part I, cf. Colloq. Math. 102, No. 2, 181--195 (2005; Zbl 1143.11346).
- University of Graz Austria
Extremal problems in graph theory, Finite abelian groups, edge disjoint cycles, Exact enumeration problems, generating functions, block monoid, factorizations of distinct lengths, Units and factorization, factorizations, Other results on the distribution of values or the characterization of arithmetic functions, half-factorial, Other analytic theory, zero-sum sequence
Extremal problems in graph theory, Finite abelian groups, edge disjoint cycles, Exact enumeration problems, generating functions, block monoid, factorizations of distinct lengths, Units and factorization, factorizations, Other results on the distribution of values or the characterization of arithmetic functions, half-factorial, Other analytic theory, zero-sum sequence
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!