Dickson–Stirling numbers
Copyright policy )Dickson–Stirling numbers
The Dickson polynomialDn, (x,a) of degreenis defined bydenotes the greatest integer function. In particular, we defineD0(x,a) = 2 for all realxanda. By using Dickson polynomials we present new types of generalized Stirling numbers of the first and second kinds. Some basic properties of these numbers and a combinatorial application to the enumeration of functions on finite sets in terms of their range values is also given.
- Pennsylvania State University United States
- Dalian Polytechnic University China (People's Republic of)
Dickson polynomials, Binomial coefficients; factorials; \(q\)-identities, generalized Stirling numbers, Exact enumeration problems, generating functions, Bell and Stirling numbers, Factorials, binomial coefficients, combinatorial functions, enumeration of functions on finite sets, Polynomials over finite fields
Dickson polynomials, Binomial coefficients; factorials; \(q\)-identities, generalized Stirling numbers, Exact enumeration problems, generating functions, Bell and Stirling numbers, Factorials, binomial coefficients, combinatorial functions, enumeration of functions on finite sets, Polynomials over finite fields
citations 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).7 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).Top 10% 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!