Face Rings of Cycles, Associahedra, and Standard Young Tableaux
نویسندگان
چکیده
منابع مشابه
Face Rings of Cycles, Associahedra, and Standard Young Tableaux
We show that Jn, the Stanley-Reisner ideal of the n-cycle, has a free resolution supported on the (n−3)-dimensional simplicial associahedron An. This resolution is not minimal for n > 6; in this case the Betti numbers of Jn are strictly smaller than the f -vector of An. We show that in fact the Betti numbers βd of Jn are in bijection with the number of standard Young tableaux of shape (d + 1, 2...
متن کاملPolygon Dissections and Standard Young Tableaux
A simple bijection is given between dissections of a convex n gon with d diagonals not intersecting in their interiors and standard Young tableaux of shape d d n d Partially supported by National Science Foundation grant DMS For d n let f n d be the number of ways to draw d diagonals in a convex n gon such that no two diagonals intersect in their interior For instance f n n is just the Catalan ...
متن کاملStandard Young tableaux and colored Motzkin paths
In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the n-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length n. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most 2d+ 1 rows and the set of ...
متن کاملEnumeration of Semi { Standard Young Tableaux
Standard tableaux. A Young tableau (also known as a standard tableau) is an arrangement of distinct integers in an array of left justiied rows, such that the entries of each row are in increasing order from left to right and the entries of each column are in increasing order from bottom to top 2. For instance, here is an array of size 15: 11 4 8 12 14 3 6 7 13 1 2 5 9 10 15 : In general a table...
متن کاملStandard Young tableaux for nite root systems
The study of representations of aane Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any nite Coxeter group. This paper is completely independent of aane Hecke algebra theory and is purely combinatorial. We deene generalized shapes and standard Young tableaux and show that these new objects coincide with the classical ones for root...
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: 2016
ISSN: 1077-8926
DOI: 10.37236/5208