New bounds on the number of representation of as a binomial coefficient.
On solving games constructed using both short and long conjunctive sums.
Improved bounds on the number of ways of expressing as a binomial coefficient.
On the number of ways of writing as a product of factorials.
On the -modules generated by partitions of a given shape.
Weak mixing of a transformation similar to Pascal
We construct a class of transformations similar to the Pascal transformation, except for the use of spacers, and show that these transformations are weakly mixing.
Minimal -universality criteria may vary in size
In this note, we give simple examples of sets of quadratic forms that have minimal -universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh [KKO05] in the negative.
Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations
We define a class of discrete Abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply recurrent. We then study conditions sufficient for showing that Cartesian products of transformations are conservative for a class of invertible infinite measure-preserving transformations and provide examples of these transformations.
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