Free quasi-symmetric functions, product actions and quantum field theory of partitions.
Frequency planning and ramifications of coloring
This paper surveys frequency assignment problems coming up in planning wireless communication services. It particularly focuses on cellular mobile phone systems such as GSM, a technology that revolutionizes communication. Traditional vertex coloring provides a conceptual framework for the mathematical modeling of many frequency planning problems. This basic form, however, needs various extensions to cover technical and organizational side constraints. Among these ramifications are T-coloring and...
Frequency squares and affine designs.
Frobenius numbers by lattice point enumeration.
Frobenius symbols for partitions and degrees of spin characters.
From -Motzkin paths to Schröder paths.
From a 1-rotational RBIBD to a partitioned difference family.
From a Ramsey-type theorem to indepedence
From Covering Designs to Graphs.
From double Hecke algebra to analysis.
From factorizations of noncommutative polynomials to combinatorial topology
This is an extended version of a talk given by the author at the conference “Algebra and Topology in Interaction” on the occasion of the 70th Anniversary of D.B. Fuchs at UC Davis in September 2009. It is a brief survey of an area originated around 1995 by I. Gelfand and the speaker.
From graphs to tensegrity structures: geometric and symbolic approaches.
A form-finding problem for tensegrity structures is studied; given an abstract graph, we show an algorithm to provide a necessary condition for it to be the underlying graph of a tensegrity in Rd (typically d=2,3) with vertices in general position. Furthermore, for a certain class of graphs our algorithm allows to obtain necessary and sufficient conditions on the relative position of the vertices in order to underlie a tensegrity, for what we propose both a geometric and a symbolic approach.
From L. Euler to D. König
Starting from the famous Königsberg bridge problem which Euler described in 1736, we intend to show that some results obtained 180 years later by König are very close to Euler's discoveries.
From paths to stars.
From recursions to asymptotics: On Szekeres' formula for the number of partitions.
Front-divisors of trees.
Frucht’s Theorem for the Digraph Factorial
To every graph (or digraph) A, there is an associated automorphism group Aut(A). Frucht’s theorem asserts the converse association; that for any finite group G there is a graph (or digraph) A for which Aut(A) ∼= G. A new operation on digraphs was introduced recently as an aid in solving certain questions regarding cancellation over the direct product of digraphs. Given a digraph A, its factorial A! is certain digraph whose vertex set is the permutations of V (A). The arc set E(A!) forms a group,...
Fruit salad.
Frutex y caminos nodales.
Dado un grafo G = (X,E) con un solo vértice insaturado p, se estudia el problema de encontrar, para todo x ∈ X, un camino M-alternado par que una x con p. Se halla un algoritmo, y se plantea su aplicación cara a dar una variante del Algoritmo de Edmonds en la que no haya que contraer los pseudovértices.
Fuchsian differential equation for the perimeter generating function of three-choice polygons.