The problem of counting monomer-dimer coverings of a lattice is a longstanding problem in statistical mechanics. It has only been exactly solved for the special case of dimer coverings in two dimensions ((Kas61), (TF61)). In earlier work, Stanley (Sta85) proved a reciprocity principle governing the number N(m,n) of dimer coverings of an m by n rectangular grid (also known as perfect matchings),...

This paper provides Closed-form expressions for the average channel capacity and probability of outage of dual-branch Selection Combining (SC) over uncorrelated Nakagami-0.5 fading channels. This channel capacity and probability of outage are evaluated under Optimum Power with Rate Adaptation (OPRA) and Truncated Channel Inversion with Fixed Rate transmission (TIFR) schemes. Since, the channel ...

defines a second-order process whenever {z¿} converges to a zero y of f(z) of multiplicity k. The process defined by equation (2) leaves two problems unsolved: (i) In practice k and y are usually not known,* (ii) The ultimate accuracy of the approximation to 7 is limited by the fact that /(«<), f'(Zi) —* 0 as z¿ —> y, provided k S; 2. The unified process, which was developed to meet both of the...

We investigate rational relations over trees. Our starting point is the definition of rational tree relations via rational expressions byRaoult (Bull. Belg.Math. Soc. 1997). We develop a new class of automata, called asynchronous tree automata, which recognize exactly these relations. The automata theoretic approach is convenient for the solution of algorithmic problems (like the emptiness prob...

A word on a nite alphabet A is said to be overlap free if it contains no factor of the form xuxux where x is a letter and u a possibly empty word In this paper we study the number un of overlap free binary words of length n which is known to be bounded by a polynomial in n First we describe a bijection between the set of overlap free words and a rational language This yields recurrence relation...

Motivated by recent results in mathematical virology, we present novel asymmetric Z[τ]-integer-valued affine extensions of the non-crystallographic Coxeter groups H2, H3 and H4 derived in a Kac-Moody-type formalism. In particular, we show that the affine reflection planes which extend the Coxeter group H3 generate (twist) translations along 2-, 3and 5-fold axes of icosahedral symmetry, and we c...

Chomsky and Schützenberger showed in 1963 that the sequence dL(n), which counts the number of words of a given length n in a regular language L, satisfies a linear recurrence relation with constant coefficients for n, i.e., it is C-finite. It follows that every sequence s(n) which satisfies a linear recurrence relation with constant coefficients can be represented as dL1 (n)− dL2 (n) for two re...

A random vector X with representation X = ∑ j≥0 AjZj is considered. Here, (Zj) is a sequence of independent and identically distributed random vectors and (Aj) is a sequence of random matrices, ‘predictable’ with respect to the sequence (Zj). The distribution of Z1 is assumed to be multivariate regular varying. Moment conditions on the matrices (Aj) are determined under which the distribution o...