In this paper we give a simple algorithm to generate all partitions of {1, 2, · · · , n} into k non-empty subsets. The number of such partitions is known as the Stirling number of the second kind. The algorithm generates each partition in constant time without repetition. By choosing k = 1, 2, · · · , n we can also generate all partitions of {1, 2, · · · , n} into subsets. The number of such pa...

Stirling numbers of the second kind and Bell numbers for graphs were defined by Duncan and Peele in 2009. In a previous paper, one of us, jointly with Nyul, extended the known results for these special numbers by giving new identities, and provided a list of explicit expressions for Stirling numbers of the second kind and Bell numbers for particular graphs. In this work we introduce q-Stirling ...

1Occupational and Environmental Health Research Group, Centre for Public Health and Population Health Research, University of Stirling, Scotland, Stirling FK9 4LA, UK 2 Institute of Aquaculture, University of Stirling, Scotland, Stirling FK9 4LA, UK 3Stirling Management School, University of Stirling, Scotland, Stirling FK9 4LA, UK 4 Institute of Health and Wellbeing, University of Glasgow, Sco...

We introduce a new encoding of the face numbers of a simplicial complex, its Stirling polynomial, that has a simple expression obtained by multiplying each face number with an appropriate generalized binomial coefficient. We prove that the face numbers of the barycentric subdivision of the free join of two CW -complexes may be found by multiplying the Stirling polynomials of the barycentric sub...

A permutation σ of a multiset is called Stirling permutation if σ(s) ≥ σ(i) as soon as σ(i) = σ(j) and i < s < j. In our paper we study Stirling polynomials that arise in the generating function for descent statistics on Stirling permutations of any multiset. We develop generalizations of the classical Stirling numbers and present their combinatorial interpretations. Particularly, we apply the ...

The Stirling cycle and related terminology is defined. Selected contemporary research involving the cycle in environmentally friendly applications is cited. Three conventional engine configurations that utilize a reciprocating power piston and crank shaft (the Alpha, Beta, and Gamma) are characterized, in terms of minimum number of components, advantages, and disadvantages. A new type of Stirli...

Application of finite element method and heat conductivity transfer model for calculation of temperature distribution in receiver for dish-Stirling concentrating solar system is described. The method yields discretized equations that are entirely local to the elements and provides complete geometric flexibility. A computer program solving the finite element method problem is created and great n...

We introduce a generalization of the Stirling numbers called the V-Stirling numbers which are inspired by the symmetric function form of the p, q-binomial coefficients. A number of properties are derived, including recurrence relations, generating functions, orthogonality relations and convolution formulas. The results are used to derive properties of some special cases and provide alternative ...