Plane partitions of shifted double staircase shape
نویسندگان
چکیده
We give a product formula for the number of shifted plane partitions double staircase shape with bounded entries. This is first new example family shapes partition in many years. The proof based on theory lozenge tilings; specifically, we apply “free boundary” Kuo condensation due to Ciucu.
منابع مشابه
Generating functions for shifted plane partitions
With the help of a tableaux method, determinant formulas for trace generating functions for various classes of shifted plane partitions are derived. Proceeding from these determinants, generalizations of Gansner's (J. hook formulas for shifted plane partitions and alternative proofs of recent results of Proctor about alternating trace generating functions are given.
متن کاملPlane Partitions
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 ...
متن کاملShifted Schur Process and Asymptotics of Large Random Strict Plane Partitions
In this paper we define the shifted Schur process as a measure on sequences of strict partitions. This process is a generalization of the shifted Schur measure introduced in [TW] and [Mat] and is a shifted version of the Schur process introduced in [OR1]. We prove that the shifted Schur process defines a Pfaffian point process. We further apply this fact to compute the bulk scaling limit of the...
متن کاملSymmetries of plane partitions
We introduce a new symmetry operation, called complementation, on plane partitions whose three-dimensional diagram is contained in a given box. This operation was suggested by work of Mills, Robbins, and Rumsey. There then arise a total of ten inequivalent problems concerned with the enumeration of plane partitions with a given symmetry. Four of these ten problems had been previously considered...
متن کاملSubwords and Plane Partitions
Using the powerful machinery available for reduced words of type B, we demonstrate a bijection between centrally symmetric k-triangulations of a 2(n + k)-gon and plane partitions of height at most k in a square of size n. This bijection can be viewed as the type B analogue of a bijection for k-triangulations due to L. Serrano and C. Stump. Résumé. En utilisant la machinerie puissante pour mots ...
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: Journal of Combinatorial Theory, Series A
سال: 2021
ISSN: ['0097-3165', '1096-0899']
DOI: https://doi.org/10.1016/j.jcta.2021.105486