Combinatorial problems related to geometrically distributed random variables.
Compositions of n as alternating sequences of weakly increasing and strictly decreasing partitions
Compositions and partitions of positive integers are often studied in separate frameworks where partitions are given by q-series generating functions and compositions exhibiting specific patterns are designated by generating functions for these patterns. Here, we view compositions as alternating sequences of weakly increasing and strictly decreasing partitions (i.e. alternating blocks). We obtain generating functions for the number of such partitions in terms of the size of the composition, the...
Compositions of random functions on a finite set.
Compositions with distinct parts.
Computing tournament sequence numbers efficiently with matrix techniques.
Counting abelian squares.
Counting -polytopes with vertices.
Counting defective parking functions.
Counting graphs with different numbers of spanning trees through the counting of prime partitions
Let be the set of all integers such that there exists a connected graph on vertices with precisely spanning trees. It was shown by Sedláček that...
Counting rooted trees: the universal law .
Counting set systems by weight.
Determining lower bounds for packing densities of non-layered patterns using weighted templates.
Discrete limit laws for additive functions on the symmetric group
Inspired by probabilistic number theory, we establish necessary and sufficient conditions under which the numbers of cycles with lengths in arbitrary sets posses an asymptotic limit law. The approach can be extended to deal with the counts of components with the size constraints for other random combinatorial structures.
Distribution of segment lengths in genome rearrangements.
Durfee polynomials.
Enumeration of factorizable multi-dimensional permutations.
From recursions to asymptotics: On Szekeres' formula for the number of partitions.
Generalizations of Carlitz compositions.
Generalized descents and normality.
Grid classes and the Fibonacci dichotomy for restricted permutations.