Abstract In a 1972 paper, Germain Kreweras investigated noncrossing partitions under the
refinement order relation. His paper set the stage both for a wealth of further enumerative …

It was first observed in (F. Brenti, Mem. Amer. Math. Soc. 413, 1989) that Pólya frequency
sequences arise often in combinatorics. In this work we point out that the same is true, more …

Stirling numbers of the first and second kind, which respectively count permutations in the
symmetric group and partitions of a set, have found extensive application in combinatorics …

We find Stieltjes-type and Jacobi-type continued fractions for some “master polynomials” that
enumerate permutations, set partitions or perfect matchings with a large (sometimes infinite) …

We consider juggling patterns where the juggler can only catch and throw one ball at a time,
and patterns where the juggler can handle many balls at the same time. Using a crossing …

Using group actions and generating functions, we derive various arithmetic properties of the
q-binomial coefficients and q-Stirling numbers. These include recurrence relations and …

The study of patterns in permutations in a very active area of current research. Klazar
defined and studied an analogous notion of pattern for set partitions. We continue this work …

In this paper we study permutations of the multiset {1 r, 2 r,…, nr}, which generalizes Gessel
and Stanley's work (J. Combin. Theory Ser. A24 (1978), 24–33) on certain permutations on …

The q-Stirling numbers (polynomials) of the second kind have been investigated and
applied in a variety of research subjects including, even, the q-analogue of Bernstein …

The Applications of Total Positivity to Combinatorics, and Conversely Page 1 The Applications
of Total Positivity to Combinatorics, and Conversely F. Brenti Abstract. Total positivity arises …