Plane Partitions

نویسنده

  • ANNA ZINK
چکیده

Throughout our study of the enumeration of plane partitions we make use of bijective proofs to find generating functions. In particular, we consider bounded plane partitions, symmetric plane partitions and weak reverse plane partitions. Using the combinatorial interpretations of Schur functions in relation to semistandard Young tableaux, we rely on the properties of symmetric functions. In our paper we will walk through some of these bijections and present the corresponding generating functions.

برای دانلود رایگان 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

Self-complementary Plane Partitions by Proctor's Minuscule Method

A method of Proctor [4] realizes the set of arbitrary plane partitions in a box and the set of symmetric plane partitions as bases of linear representations of Lie groups. We extend this method by realizing transposition and complementation of plane partitions as natural linear transformations of the representations, thereby enumerating symmetric plane partitions, self-complementary plane parti...

متن کامل

Random Sampling of Plane Partitions

This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are slightly superlinear: the complexity is O(n(lnn)3) in approximate-size sampling and O(n4/3) in exact-size sampling (under a real-arithmetic computation mode...

متن کامل

(−1)–enumeration of Plane Partitions with Complementation Symmetry

We compute the weighted enumeration of plane partitions contained in a given box with complementation symmetry where adding one half of an orbit of cubes and removing the other half of the orbit changes the weight by −1 as proposed by Kuperberg in [7, pp.25/26]. We use nonintersecting lattice path families to accomplish this for transpose–complementary, cyclically symmetric transpose–complement...

متن کامل

On P-partitions related to ordinal sums of posets

Using the inclusion–exclusion principle, we derive a formula of generating functions for P-partitions related to ordinal sums of posets. This formula simplifies computations for many variations of plane partitions, such as plane partition polygons and plane partitions with diagonals or double diagonals. We illustrate our method by several examples, some of which are new variations of plane part...

متن کامل

On Powers of 2 Dividing the Values of Certain Plane Partition Functions

We consider two families of plane partitions: totally symmetric self-complementary plane partitions (TSSCPPs) and cyclically symmetric transpose complement plane partitions (CSTCPPs). If T (n) and C(n) are the numbers of such plane partitions in a 2n× 2n× 2n box, then ord2(T (n)) = ord2(C(n)) for all n ≥ 1. We also discuss various consequences, along with other results on ord2(T (n)). 2000 Math...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011