Related papers: Algebraic and geometric methods in enumerative com…
This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of…
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
A categorized bibliography of combinators is given, providing what is believed to be a largely complete coverage of publications from the origination of combinators in 1920 to the present day.
A procedure for the algebraization of a $CR$-manifold and its holomorphic automorphisms is described. Examples of the application of algebraization are considered. Questions arising in connection with the algebraization of a $CR$-manifold…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on independent subsets of powers of paths and cycles, trying to…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…
A method of local approximation of holomorphic solutions of algebraic equations is discussed
This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
In terms of the derivative operator and three hypergeometric series identities, several interesting summation formulas involving generalized harmonic numbers are established.
An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
We study the square of opposition and its various geometric generalizations from an algebraic viewpoint. In particular, we show how the various shapes of oppositions can be framed under an algebraic framework and we illustrate this approach…
A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.
This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…