Some applications of S-restricted set partitions

Bényi, Beáta; Ramírez, José L.

doi:10.1007/s10998-018-0252-1

Cited by 9 publications

(9 citation statements)

References 35 publications

(45 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a series of papers about Stirling numbers [2,3,4] the authors studied the underlying objects, partitions, permutations and lists with the extra condition on the size of the sets, cycles and lists, respectively. For the sake of a comprehensive study of mixed Stirling numbers of the first kind, we follow this idea and derive some results for the number of mixed permutations such that each cycle has length s contained in a given set of integers S. These general results include many interesting cases that can be easily obtained by special settings of S, as for instance, S = {1, 2, .…”

Section: S-restricted Stirling Number Of the First Kindmentioning

confidence: 99%

Mixed coloured permutations

Bényi

Yaqubi

2020

Proc Math Sci

Self Cite

View full text Add to dashboard Cite

In this paper we introduce mixed coloured permutation, permutations with certain coloured cycles, and study the enumerative properties of these combinatorial objects. We derive the generating function, closed forms, recursions and combinatorial identities for the counting sequence, mixed Stirling numbers of the first kind. In this comprehensive study we consider further the conditions on the length of the cycles, r-mixed Stirling numbers and the connection to Bell polynomials.2010 Mathematics Subject Classification. 05A18, 11B73.

show abstract

Section: S-restricted Stirling Number Of the First Kindmentioning

confidence: 99%

Mixed coloured permutations

Bényi

Yaqubi

2020

Proc Math Sci

Self Cite

View full text Add to dashboard Cite

show abstract

“…Remark 2. The recent author investigates with J. L. Ramrez lonesum matrices with further restrictions on the number of columns and rows of the same type in a forthcoming paper [11].…”

Section: The Proof Of the Main Theoremmentioning

confidence: 99%

Restricted lonesum matrices

Bényi¹

2018

AMI

Self Cite

View full text Add to dashboard Cite

Lonesum matrices are matrices that are uniquely reconstructible from their row and column sum vectors. These matrices are enumerated by the poly-Bernoulli numbers; a sequence related to the multiple zeta values with a rich literature in number theory. Lonesum matrices are in bijection with many other combinatorial objects: several permutation classes, matrix classes, acyclic orientations in complete bipartite graphs etc. Motivated of these facts, we study in this paper lonesum matrices with restriction on the number of columns and rows of the same type.

show abstract

“…In another direction, using the formula of poly-Bernoulli numbers, that involves the Stirling numbers of the second kind, the authors replaced in the formula variations of the Stirling numbers and studied the so obtained number sequences and polynomials, respectively. For example, the classical Stirling numbers are replaced by the incomplete Stirling numbers [11,24] or the r-Stirling numbers [10,25].…”

Section: Introductionmentioning

confidence: 99%