搜索结果: 1-9 共查到“组合数学 functions”相关记录9条 . 查询时间(0.09 秒)
Lattice-point generating functions for free sums of convex sets
Lattice-point generating functions free sums of convex sets Combinatorics
2012/7/11
Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give expressions for the generating...
Lattice Point Generating Functions and Symmetric Cones
Lattice Point Generating Functions Symmetric Cones Combinatorics
2012/6/29
We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones th...
Divided Differences of Multivariate Implicit Functions
Divided Differences Multivariate Implicit Functions Numerical Analysis Combinatorics
2012/3/1
Under general conditions, the equation $g(x^1, ..., x^q, y) = 0$ implicitly defines $y$ locally as a function of $x^1, ..., x^q$. In this article, we express divided differences of $y$ in terms of div...
Crystal energy functions via the charge in types A and C
Crystal energy functions Combinatorics
2011/9/16
Abstract: The Ram-Yip formula for Macdonald polynomials (at t=0) provides a statistic which we call charge. In types A and C it can be defined on tensor products of Kashiwara-Nakashima single column c...
Redundant generating functions in lattice path enumeration
lattice path enumeration Combinatorics Redundant generating functions
2011/9/15
Abstract: A redundant generating function is a generating function having terms which are not part of the solution of the original problem. We use redundant generating functions to study two path prob...
Expansion of $k$-Schur functions for maximal $k$-rectangles within the affine nilCoxeter algebra
$k$-Schur functions $k$-rectangles affine nilCoxeter algebra Combinatorics
2011/9/14
Abstract: We give several explicit combinatorial formulas for the expansion of $k$-Schur functions indexed by maximal $k$-rectangles, $s_R^{(k)}$, in terms of the standard basis of the affine nilCoxet...
Sums of Ceiling Functions Solve Nested Recursions
Nested recursion Ceiling function Formal satisfaction Equivalence class
2011/9/15
Abstract: It is known that, for given integers s \geq 0 and j > 0, the nested recursion R(n) = R(n - s - R(n - j)) + R(n - 2j - s - R(n - 3j)) has a closed form solution for which a combinatorial inte...
On the functions counting walks with small steps in the quarter plane
Walks in the quarter plane counting generating function holonomy group of the walk Riemann surface elliptic functions
2011/9/5
Abstract: Models of spatially homogeneous walks in the quarter plane with steps taken from the eight nearest neighbors are considered. Counting function $(x,y,z)\mapsto Q(x,y;z)$ of the numbers $q(i,j...
Loop symmetric functions and factorizing matrix polynomials
Loop symmetric functions factorizing matrix polynomials
2011/1/18
These are notes for my talk at ICCM 2010, Beijing. We survey some results, obtained jointly with Pavlo Pylyavskyy, concerning the ring of loop symmetric functions. Motivations from networks on surface...