Related papers: Eulerian pairs on Fibonacci words

In this paper a new approach is derived in the context of shape theory. The implemented methodology is motivated in an open problem proposed in \citet{GM93} about the construction of certain shape density involving Euler hypergeometric…

For a pair (algebra, module) with equidimensional and isolated singularity we establish the existence of a versal henselian deformation. Obstruction theory in terms of an Andr\'e-Quillen cohomology for pairs is a central ingredient in the…

Gross, Mansour and Tucker introduced the partial-dual orientable genus polynomial and the partial-dual Euler genus polynomial. They computed these two partial-dual genus polynomials of four families of ribbon graphs, posed some research…

We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference…

We generalize Merel's work on universal Fourier expansions to Bianchi modular forms over Euclidean imaginary quadratic fields, under the assumption of the nondegeneracy of a pairing between Bianchi modular forms and Bianchi modular symbols.…

We study decreasing binary trees in which every vertex with two children is colored red or blue. We construct two bijections. The first, to ordered set partitions into odd-sized blocks each arranged as an alternating permutation, shows that…

Permutation-partition pairs were introduced by Stahl in 1980. These pairs are generalizations of graphs and graphs on surfaces. They were used to solve some problems for orientable embeddings of graphs. In this paper, we introduce a…

We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another…

On the set of permutations of a finite set, we construct a bijection which maps the 3-vector of statistics $(maj-exc,des,exc)$ to a 3-vector $(maj\_2,\widetilde{des\_2},inv\_2)$ associated with the $q$-Eulerian polynomials introduced by…

In this paper, we provide new applications of Fibonacci and Lucas numbers. In some circumstances, we find algebraic structures on some sets defined with these numbers, we generalize Fibonacci and Lucas numbers by using an arbitrary binary…

In this article we prove a Howe correspondence for a family of representations of sl(2n), which was introduced by Benkart, Britten, and Lemire.

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented…

Several specific Franklin squares and magic squares are decomposed into their quotient and remainder squares. The results support the conjecture that Franklin used the Eulerian composition method to construct many of his squares. This…

The hyperbolic Pascal triangle ${\cal HPT}_{4,q}$ $(q\ge5)$ is a new mathematical construction, which is a geometrical generalization of Pascal's arithmetical triangle. In the present study we show that a natural pattern of rows of ${\cal…

In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian…

We present some Pfaffian identities, which are completely different from the Pl\"ucker relations. As consequences we obtain a quadratic identity for the number of perfect matchings of plane graphs, which has a simpler form than the formula…

Mignosi, Restivo, and Salemi (1998) proved that for all $\epsilon > 0$ there exists an integer $N$ such that all prefixes of the Fibonacci word of length $\geq N$ contain a suffix of exponent $\alpha^2-\epsilon$, where $\alpha =…

In the very early universe, a generalized Schwinger effect can create pairs from both electrical and gravitational fields. The expectation value of fermionic current induced by these newly created pairs has been recently computed in de…

Powers of Fibonacci polynomials are expressed as single sums, improving on a double sum recently seen in the literature.

Gross, Mansour and Tucker introduced the partial-dual orientable genus polynomial and the partial-dual Euler genus polynomial. They showed that the partial-dual genus polynomial for an orientable ribbon graph is interpolating and gave an…