Yingrui Zhang

activity

20182024

k

-Dyck paths

1 citations · 1 across the 8 of their papers we have counts for

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8 papers · 1 filter

math.CO2024

A Combinatorial Decomposition of Knapsack Cones

Guoce Xin, Yingrui Zhang, Zihao Zhang

In this paper, we focus on knapsack cones, a specific type of simplicial cones that arise naturally in the context of the knapsack problem $x_{1} a_{1} + \dots + x_{n} a_{n} = a_{0}$ . We pr…

math.CO2023

Inverting the General Order Sweep Map

Ying Wang, Guoce Xin, Yingrui Zhang

Building upon the foundational work of Thomas and Williams on the modular sweep map, Garsia and Xin have developed a straightforward algorithm for the inversion of the sweep map on…

math.CO2023

Algebraic Volume for Polytope Arise from Ehrhart Theory

Guoce Xin, Xinyu Xu, Yingrui Zhang +1

Volume computation for $d$ -polytopes $P$ is fundamental in mathematics. There are known volume computation algorithms, mostly based on triangulation or signed-decompositi…

math.CO2023

Fast Evaluation of Generalized Todd Polynomials: Applications to MacMahon's Partition Analysis and Integer Programming

Guoce Xin, Yingrui Zhang, ZiHao Zhang

The Todd polynomials, denoted as $t d_{k} (b_{1}, b_{2}, \dots, b_{m})$ , are characterised by their generating functions: $k \geq 0 \sum t d_{k} s^{k} = i = 1 \prod m \frac{b _{i} s}{e ^{b_{i} s} - 1} .$ …

math.CO2021

Enumerating Magic Distinct Labellings of the Cube

Guoce Xin, Yingrui Zhang, Zihao Zhang

We find by applying MacMahon's partition analysis that all magic labellings of the cube are of eight types, each generated by six basis elements. A combinatorial proof of this fact…

math.CO2021

The $q, t$ -symmetry of the generalized $q, t$ -Catalan number $C_{(k_{1}, k_{2}, k_{3})} (q, t)$ and $C_{(k, k, k, k)} (q, t)$

Guoce Xin, Yingrui Zhang

We give two proofs of the $q, t$ -symmetry of the generalized $q, t$ -Catalan number $C_{k} (q, t)$ for $k = (k_{1}, k_{2}, k_{3})$ . One is by using MacMahon's partition analysis as we…

math.CO2020★ 1 cited

Dinv, Area, and Bounce for $k$ -Dyck paths

Guoce Xin, Yingrui Zhang

The well-known $q, t$ -Catalan sequence has two combinatorial interpretations as weighted sums of ordinary Dyck paths: one is Haglund's area-bounce formula, and the other is Haiman's…

math.CO2018

On the Sweep Map for $k$ -Dyck Paths

Guoce Xin, Yingrui Zhang

Garsia and Xin gave a linear algorithm for inverting the sweep map for Fuss rational Dyck paths in $D_{m, n}$ where $m = k n \pm 1$ . They introduced an intermediate family $\mathcal{T}_…

A Combinatorial Decomposition of Knapsack Cones

Inverting the General Order Sweep Map

Algebraic Volume for Polytope Arise from Ehrhart Theory

Fast Evaluation of Generalized Todd Polynomials: Applications to MacMahon's Partition Analysis and Integer Programming

Enumerating Magic Distinct Labellings of the Cube

The q,t-symmetry of the generalized q,t-Catalan number C(k1​,k2​,k3​)​(q,t) and C(k,k,k,k)​(q,t)

Dinv, Area, and Bounce for k-Dyck paths

On the Sweep Map for k-Dyck Paths

The $q, t$ -symmetry of the generalized $q, t$ -Catalan number $C_{(k_{1}, k_{2}, k_{3})} (q, t)$ and $C_{(k, k, k, k)} (q, t)$

Dinv, Area, and Bounce for $k$ -Dyck paths

On the Sweep Map for $k$ -Dyck Paths