Lecture Hall Partitions and the Affine Hyperoctahedral Group
نویسندگان
چکیده
منابع مشابه
Lecture Hall Partitions and the Affine Hyperoctahedral Group
In 1997 Bousquet-Mélou and Eriksson introduced lecture hall partitions as the inversion vectors of elements of the parabolic quotient C̃/C. We provide a new view of their correspondence that allows results in one domain to be translated into the other. We determine the equivalence between combinatorial statistics in each domain and use this correspondence to translate certain generating function...
متن کاملLecture hall partitions and the wreath products
It is shown that statistics on the wreath product groups, Ck oSn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck oSn. Finally, some new statistics on Ck oSn are introduced, inspired by lecture hall theory, and their distributions are derived.
متن کاملThe mathematics of lecture hall partitions
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to lecture hall partitions have used polyhedral geometry to discover further properties of these rich combinatorial objects. In this paper we give an overview of s...
متن کاملThe Hyperoctahedral Quantum Group
We present a definition for free quantum groups. The idea is that these must satisfy S n ⊂ G ⊂ U + n , along with a technical representation theory condition. We work out in detail the case of quantum analogues of the hyperoctahedral group Hn. We first consider the hypercube in R , and show that its quantum symmetry group is in fact a q-deformation of On at q = −1. Then we consider the space fo...
متن کاملOn q-series Identities Arising from Lecture Hall Partitions
In this paper, we highlight two q-series identities arising from the “five guidelines” approach to enumerating lecture hall partitions and give direct, qseries proofs. This requires two new finite corollaries of a q-analog of Gauss’s second theorem. In fact, the method reveals stronger results about lecture hall partitions and anti-lecture hall compositions that are only partially explained com...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7201