Affine permutations and rational slope parking functions
نویسندگان
چکیده
منابع مشابه
Coding Parking Functions by Pairs of Permutations
We introduce a new class of admissible pairs of triangular sequences and prove a bijection between the set of admissible pairs of triangular sequences of length n and the set of parking functions of length n. For all u and v = 0, 1, 2, 3 and all n ≤ 7 we describe in terms of admissible pairs the dimensions of the bi-graded components hu,v of diagonal harmonics C[x1, . . . , xn; y1, . . . , yn]/...
متن کاملAffine Permutations and an Affine Coxeter Monoid
In this expository paper, we describe results on pattern avoidance arising from the affine Catalan monoid. The schema of affine codes as canonical decompositions in conjunction with two-row moves is detailed, and then applied in studying the Catalan quotient of the 0-Hecke monoid. We prove a conjecture of Hanusa and Jones concerning periodicity in the number of fully-commutative affine permutat...
متن کاملDiagrams of affine permutations , balanced labellings , and affine Stanley symmetric functions (
We study the diagrams of affine permutations and their balanced labellings. As in the finite case, which was investigated by Fomin, Greene, Reiner, and Shimozono, the balanced labellings give a natural encoding of reduced decompositions of affine permutations. In fact, we show that the sum of weight monomials of the column strict balanced labellings is the affine Stanley symmetric function defi...
متن کاملCanonical Decompositions of Affine Permutations, Affine Codes, and Split k-Schur Functions
We develop a new perspective on the unique maximal decomposition of an arbitrary affine permutation into a product of cyclically decreasing elements, implicit in work of Thomas Lam [Lam06]. This decomposition is closely related to the affine code, which generalizes the kbounded partition associated to Grassmannian elements. We also prove that the affine code readily encodes a number of basic co...
متن کاملAffine Permutations and Inversion Multigraphs
In this paper we solve the problem of characterizing inversion multi-graphs (cf. BB]) associated to aane permutations.
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: Transactions of the American Mathematical Society
سال: 2016
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6584