相关论文: A species approach to Rota's twelvefold way
In this note we present a method for obtaining a wide class of combinatorial identities. We give several examples, in particular, based on the Gamma and Beta functions. Some of them have already been considered by previously, and other are…
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets, and to provide computational tools for multipath…
We obtain a differential equation for the enumeration of the path length of general increasing trees. By using differential operators and their combinatorial interpretation we give a bijective proof of a version of Fa\`a di Bruno formula,…
General revision. In particular the parts concerning involutive bases over rings have been significantly changed. In addition some proofs have been improved.
We generalize first-species counterpoint theory to arbitrary rings and obtain some new counting and maximization results that enrich the theory of admitted successors, pointing to a structural approach, beyond computations. The…
We discuss the recent results of the author on the existence of systems of differential equations for chiral genus-zero and genus-one correlation functions in conformal field theories.
Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
We obtain an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of ramification points, and conjecture this to be true for an arbitrary number of ramification…
The causal set theory d'Alembertian has rational coefficients for which alternating expressions are known. Here, a combinatorial interpretation of these numbers is given.
We describe combinatorial aspects of classical resolution of singularities that are free of characteristic and can be applied to singular foliations and vector fields as well as to functions and varieties. In particular, we give a…
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…
The aim of this note is to show the existence of a large family of Cantorvals arising in the projection description of primitive two-letter substitutions. This provides a common and naturally occurring class of Cantorvals.
The use of algebraic tools of operational and umbral nature is exploited to develop a new point of view and to extend the theory of Hermite polynomials, with more than one variable also of complex nature. The techniques we adopt includes…
In [Dugan-Glennon-Gunnells-Steingrimsson-2019], the authors introduce tiered trees to define combinatorial objects counting absolutely indecomposable representations of certain quivers, and torus orbits on certain homogeneous varieties. In…
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
Meadows - commutative rings equipped with a total inversion operation - can be axiomatized by purely equational means. We study subvarieties of the variety of meadows obtained by extending the equational theory and expanding the signature.
Chow rings of toric varieties, which originate in intersection theory, feature a rich combinatorial structure of independent interest. We survey four different ways of computing in these rings, due to Billera, Brion, Fulton--Sturmfels, and…
Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…
This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of naturalduality are employed to give, economically and in a uniform way, categories ofstructures dually…