Chromatic Statistics for Triangulations and Fuß-Catalan Complexes
نویسندگان
چکیده
We introduce Fuß–Catalan complexes as d-dimensional generalisations of triangulations of a convex polygon. These complexes are used to refine Catalan numbers and Fuß–Catalan numbers, by introducing colour statistics for triangulations and Fuß–Catalan complexes. Our refinements consist in showing that the number of triangulations, respectively of Fuß–Catalan complexes, with a given colour distribution of its vertices is given by closed product formulae. The crucial ingredient in the proof is the Lagrange–Good inversion formula.
منابع مشابه
q, t-Fuß-Catalan numbers for complex reflection groups
In type A, the q, t-Fuß-Catalan numbers Cat n (q, t) can be defined as a bigraded Hilbert series of a module associated to the symmetric group Sn. We generalize this construction to (finite) complex reflection groups and exhibit some nice conjectured algebraic and combinatorial properties of these polynomials in q and t. Finally, we present an idea how these polynomials could be related to some...
متن کاملq, t-Fuß–Catalan numbers for finite reflection groups
In type A, the q, t-Fuß–Catalan numbers can be defined as the bigraded Hilbert series of a module associated to the symmetric group. We generalize this construction to (finite) complex reflection groups and, based on computer experiments, we exhibit several conjectured algebraic and combinatorial properties of these polynomials with nonnegative integer coefficients. We prove the conjectures for...
متن کاملq, t-FUSS-CATALAN NUMBERS FOR COMPLEX REFLECTION GROUPS
In type A, the q, t-Fuß-Catalan numbers Cat (m) n (q, t) can be defined as a bigraded Hilbert series of a module associated to the symmetric group Sn. We generalize this construction to (finite) complex reflection groups and exhibit some nice conjectured algebraic and combinatorial properties of these polynomials in q and t. Finally, we present an idea how these polynomials could be related to ...
متن کاملOn the H-triangle of generalised nonnesting partitions
With a crystallographic root system Φ, there are associated two Catalan objects, the set of nonnesting partitions NN(Φ), and the cluster complex ∆(Φ). These possess a number of enumerative coincidences, many of which are captured in a surprising identity, first conjectured by Chapoton. We prove this conjecture, and indicate its generalisation for the Fuß-Catalan objects NN (Φ) and ∆(Φ), conject...
متن کاملCatalan Triangulations of the M Obius
A Catalan triangulation of the MM obius band is an abstract simplicial complex triangulating the MM obius band which uses no interior vertices, and has vertices labelled 1; 2; : : : ; n in order as one traverses the boundary. We prove two results about the structure of this set, analogous to well-known results for Catalan triangulations of the disk. The rst is a generating function for Catalan ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 18 شماره
صفحات -
تاریخ انتشار 2011