Topics in Algebraic Combinatorics

نویسنده

  • Richard P. Stanley
چکیده

. We think that if φ(e) = uv (short for {u, v}), then e connects u and v or equivalently e is incident to u and v. If there is at least one edge incident to u and v then we say that the vertices u and v are adjacent. If φ(e) = vv, then we call e a loop at v. If several edges e1, . . . , ej (j > 1) satisfy φ(e1) = · · · = φ(ej) = uv, then we say that there is a multiple edge between u and v. A graph without loops or multiple edges is called simple. In this case we can think of E as just a subset of ( V 2 )

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Recent Advances in Algebraic and Enumerative Combinatorics

Algebraic and enumerative combinatorics is concerned with objects that have both a combinatorial and an algebraic interpretation. It is a highly active area of the mathematical sciences, with many connections and applications to other areas, including algebraic geometry, representation theory, topology, mathematical physics and statistical mechanics. Enumerative questions arise in the mathemati...

متن کامل

Gröbner Basis Techniques in Algebraic Combinatorics

Gröbner basis techniques in the algebraic study of triangulations of convex polytopes as well as of the number of faces of simplicial complexes will be discussed. Of these two traditional topics in combinatorics, the first will be studied by using initial ideals of toric ideals and the second will be studied by using generic initial ideals of monomial ideals.

متن کامل

New interactions of Combinatorics and Probability

Algebraic Combinatorics K. Ebrahimi-Fard, ICMAT-CSIC, Madrid, Spain F. Patras, CNRS, Nice, France (3+3 hrs) – The seminal works of G.-C. Rota and his school, have transformed algebraic combinatorics into an important branch of mathematics with connections to a wide variety of subjects, among others, numerical methods for (partial/stochastic) differential equations; control theory; quantum field...

متن کامل

Chromatic Quasisymmetric Functions and Hessenberg Varieties

We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generalization of the Eulerian polynomials, the one in symmetric function theory deals with a refinement of the chromatic symmetric functions of Stanley, and the one in algebra...

متن کامل

Permutations Richard

Permutations of finite sets play a central role in algebraic and enumerative combinatorics. In addition to having many interesting enumerative properties per se, permutations also arise in almost every area of mathematics and indeed in all the sciences. Here we will discuss three different topics involving permutations, focusing on combinatorics but also giving some hints about connections with...

متن کامل

Research Statement: Combinatorial Structures in Pure and Applied Mathematics

I am a combinatorialist with diverse interests. The power of combinatorics derives from the wide applicability of its methods. Discrete structures arise throughout mathematics and science, yet all too often combinatorics is unnecessarily done in isolation. I aim to bridge the gap between combinatorics and other fields through collaborations with mathematicians and scientists from varied discipl...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013