The Catalan Threshold Arrangement

نویسنده

  • Seunghyun Seo
چکیده

Hyperplane arrangements are very interesting combinatorial objects and many results can be found in the literature. For instance, several papers [1, 2, 6, 7] are concerned with the characteristic polynomials and the number of regions of a hyperplane arrangement. In his paper [9], Stanley reviewed various hyperplane arrangements raising interesting questions, one of which is related to the following hyperplane arrangement:

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

A bijection between dominant Shi regions and core partitions

It is well-known that Catalan numbers Cn = 1 n+1 ( 2n n ) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n + 1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi a...

متن کامل

A bijection between (bounded) dominant Shi regions and core partitions

It is well-known that Catalan numbers Cn = 1 n+1 ( 2n n ) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n + 1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi a...

متن کامل

On Floors and Ceilings of the $k$-Catalan Arrangement

The set of dominant regions of the k-Catalan arrangement of a crystallographic root system Φ is a well-studied object enumerated by the Fuß-Catalan number Cat(k)(Φ). It is natural to refine this enumeration by considering floors and ceilings of dominant regions. A conjecture of Armstrong states that counting dominant regions by their number of floors of a certain height gives the same distribut...

متن کامل

Facets of the Generalized Cluster Complex and Regions in the Extended Catalan Arrangement of Type A

In this paper we present a bijection between two well known families of Catalan objects: the set of facets of the m-generalized cluster complex ∆(An) and that of dominant regions in the m-Catalan arrangement Cat(An), where m ∈ N>0. In particular, the map which we define bijects facets containing the negative simple root −α to dominant regions having the hyperplane {v ∈ V | 〈v, α〉 = m} as separa...

متن کامل

Deformations of the Braid Arrangement and Trees Dedicated to Ira Gessel for His Retirement

We establish counting formulas and bijections for deformations of the braid arrangement. Precisely, we consider real hyperplane arrangements such that all the hyperplanes are of the form xi − xj = s for some integer s. Classical examples include the braid, Catalan, Shi, semiorder and Linial arrangements, as well as graphical arrangements. We express the number of regions of any such arrangement...

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 2016