In this paper we study subdivision schemes that both interpolate and preserve the monotonicity of the input data, and we derive a simple ratio condition that guarantees the continuous differentiability of the limit function. We then show that the condition holds for both a scheme of Kuijt and van Damme, based on rational functions, and a scheme of Sabin and Dodgson, based on square roots. MSC: ...

An extensive literature exists describing various techniques for the evaluation of Hankel determinants. The prevailing methods such as Dodgson condensation, continued fraction expansion, LU decomposition, all produce product formulas when they are applicable. We mention the classic case of the Hankel determinants with binomial entries 3k+2 k and those with entries 3k k ; both of these classes o...

We speculate on whether a certain p-adic stability phenomenon, observed by David Robbins empirically for Dodgson condensation, appears in other nonlinear recurrence relations that “unexpectedly” produce integer or nearly-integer sequences. We exhibit an example (number friezes) where this phenomenon provably occurs. This note may be viewed as an addendum to Robbins’s note [5] in this volume. It...

In the preceding paper (Dodgson & Powell, 1959) it was shown that an arylsulphatase present in the digestive juice and the digestive gland of the edible snail exhibited a shift in optimum pH as the concentration of substrate was increased. This paper describes the partial purification of the digestivegland enzyme and provides further evidence that the shift in optimum pH is not due to the prese...

We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the L...

Abstract In this paper we construct a family of ternary interpolatory Hermite subdivision schemes order 1 with small support and ${\mathscr{H}}\mathcal {C}^{2}$ H C 2 -smoothness. Indeed, leaving the binary domain, it is possible ...

The widespread occurrence of sulphatases in the Mollusca was first demonstrated by Soda & Hattori (1933a, b) who showed that these enzymes are mainly concentrated in the digestive glands. That extracts from marine molluscs also possess ,B-glucuronidase activity was first noted by Dodgson, Lewis & Spencer (1952) who studied the optimum conditions for the activity ofthis enzyme and arylsulphatase...

We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the L...

The voting rules proposed by Dodgson and Young are both designed to find the alternative closest to being a Condorcet winner, according to two different notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorithms for approximating the Dodgson score: an LP-based randomized rounding algorithm and a determini...

Conflict of interest is the permanent companion of any population of agents (computational or biological). For that reason, the ability to compromise is of paramount importance, making voting a key element of societal mechanisms. One of the voting procedures most often discussed in the literature and, due to its intuitiveness, also conceptually quite appealing is Charles Dodgson’s scoring rule,...