Abstract. We investigate a (q, t)-generalization of the usual binomial and q-binomial coefficients. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These polynomials and their interpretations generalize further in two directions, one relatin...

We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to column-strict...

Abstract. We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to col...

Abstract. We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to col...

The swimming behaviours of two species of ciliates characterized by different mechanosensory and ciliary motor properties were investigated under hypergravity up to 5.4 g. The experiments were designed to examine large numbers of cells using video recording, digital data processing and statistics for the documentation of the rates and orientations of swimming. The gravikinetic responses (change...