In [12] it is shown that the probabilistic powerdomain of a continuous domain is again continuous. The category of continuous domains, however, is not cartesian closed, and one has to look at subcategories such as RB, the retracts of bifinite domains. [8] offers a proof that the probabilistic powerdomain construction can be restricted to RB. In this paper, we give a counterexample to Graham’s p...

Chung, Diaconis, and Graham considered random processes of the form Xn+1 = 2Xn + bn (mod p) where X0 = 0, p is odd, and bn for n = 0, 1, 2, . . . are i.i.d. random variables on {−1, 0, 1}. If Pr(bn = −1) = Pr(bn = 1) = β and Pr(bn = 0) = 1 − 2β, they asked which value of β makes Xn get close to uniformly distributed on the integers mod p the slowest. In this paper, we extend the results of Chun...

An important combinatorial result in equivariant cohomology and K-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work uniformly in all Lie types, and are based on the concept of a root polynomial. In this paper we define formal root polynomials associated with an arbitrary formal...

The problem we consider in the present paper is how to find the closed form of a class of combinatorial sums, if it exists. The problem is well known in the literature, and is as old as Combinatorial Analysis is, since we can go back at least to Euler’s time. More recently, Riordan has tried to give a general approach to the subject, proposing a variety of methods, many of which are related to ...

In a graph G with a distribution of pebbles on its vertices, a pebbling move is the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. A weight function on G is a nonnegative integer-valued function on the vertices of G. A distribution of pebbles on G covers a weight function if there exists a sequence of pebbling moves that gives a new distribution in ...

Results of Lovász (1972) and Padberg (1974) imply that partitionable graphs contain all the potential counterexamples to Berge’s famous Strong Perfect Graph Conjecture. A recursive method of generating partitionable graphs was suggested by Chvátal, Graham, Perold and Whitesides (1979). Results of Sebő (1996) entail that Berge’s conjecture holds for all the partitionable graphs obtained by this ...

A constant-composition code is a special constant-weight code under the restriction that each symbol should appear a given number of times in each codeword. In this correspondence, we give a lower bound for the maximum size of the -ary constant-composition codes with minimum distance at least 3. This bound is asymptotically optimal and generalizes the Graham–Sloane bound for binary constant-wei...

p non-zero residues (mod p) . Assume that if ' a i a i , ei=0 or 1 (not all e i=0) is a i=1 p multiple of p then is uniquely determined . The conjecture states that in this i=1 case there are only two distinct residues among the a's . We are going to prove this conjecture for all sufficiently large p, in fact we will prove a sharper result . To extend our proof for the small values of p would r...

We consider the question: can the isotropy representation of an irreducible pseudoRiemannian symmetric space be realized as a conformal holonomy group? Using recent results of Čap, Gover and Hammerl, we study the representations of SO(2, 1), PSU(2, 1) and PSp(2, 1) as isotropy groups of irreducible symmetric spaces of signature (3, 2), (4, 4) and (6, 8), respectively, describing the geometry in...

We apply the method of characteristics for the solution of pde's to two combinatorial problems. The first is finding an explicit form for a distribution that arises in bio-informatics. The second is a question raised by Graham, Knuth and Patashnik about a sequence of generalized binomial coefficients. We find an exact formula, which factors in an interesting way, in the case where one of the si...