Y. Au

activity

20082026

collaborators

15 papers

math.CO2026

Enumerating Multi-Operator Monomials in Commutative and Noncommutative Settings

Yu Hin Au, Murray R. Bremner

We study enumeration problems for multi-operator monomials generated from one indeterminate by an associative multiplication together with finitely many unary operators. We conside…

math.CO2025

A new generalization of the Narayana numbers inspired by linear operators on associative $d$ -ary algebras

Yu Hin Au, Murray R. Bremner

We introduce and study a generalization of the Narayana numbers $N_{d} (n, k) = \frac{1}{n + 1} (k + 1 n + 1) (k n + ( n - k ) ( d - 2 ) + 1)$ for integers $d \geq 2$ and $n, k \geq 0$ . T…

math.CO2025

A Computational Search for Minimal Obstruction Graphs for the Lovász--Schrijver SDP Hierarchy

Yu Hin Au, Levent Tunçel

We study the lift-and-project relaxations of the stable set polytope of graphs generated by $LS_{+}$ , the SDP lift-and-project operator devised by Lovász and Schrijver. Our fo…

math.CO2025

Stable Set Polytopes with Rank $∣ V (G) ∣/3$ for the Lovász--Schrijver SDP Operator

Yu Hin Au, Levent Tunçel

We study the lift-and-project rank of the stable set polytope of graphs with respect to the Lovász--Schrijver SDP operator $LS_{+}$ applied to the fractional stable set polyto…

cs.DM2024

On Rank-Monotone Graph Operations and Minimal Obstruction Graphs for the Lovász--Schrijver SDP Hierarchy

Yu Hin Au, Levent Tunçel

We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lovász--Schrijver SDP operator $LS_{+}$ , with a particular focus on finding and ch…

math.OC2023

Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operator

Yu Hin Au, Levent Tunçel

We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lovász-Schrijver SDP operator $LS_{+}$ . In particular, we focus on a search for re…

math.CO2022

Decompositions of Unit Hypercubes and the Reversion of a Generalized Möbius Series

Yu Hin Au

Let $s_{d} (n)$ be the number of distinct decompositions of the $d$ -dimensional hypercube with $n$ rectangular regions that can be obtained via a sequence of splitting operations. We…

math.CO2020

On Connections Between Association Schemes and Analyses of Polyhedral and Positive Semidefinite Lift-and-Project Relaxations

Yu Hin Au, Nathan Lindzey, Levent Tunçel

We explore some connections between association schemes and the analyses of the semidefinite programming (SDP) based convex relaxations of combinatorial optimization problems in th…

math.CO2019

Some Properties and Combinatorial Implications of Weighted Small Schröder Numbers

Yu Hin Au

The $n^{th}$ small Schröder number is $s (n) = \sum_{k \geq 0} s (n, k)$ , where $s (n, k)$ denotes the number of plane rooted trees with $n$ leaves and $k$ internal nodes that ea…

math.CO2019

Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube

Yu Hin Au, Fatemeh Bagherzadeh, Murray R. Bremner

We study a two-parameter generalization of the Catalan numbers: $C_{d, p} (n)$ is the number of ways to subdivide the $d$ -dimensional hypercube into $n$ rectangular blocks using orth…

math.OC2016

Elementary polytopes with high lift-and-project ranks for strong positive semidefinite operators

Yu Hin Au, Levent Tunçel

We consider operators acting on convex subsets of the unit hypercube. These operators are used in constructing convex relaxations of combinatorial optimization problems presented a…

math.CO2014

Notes and Note-Pairs in Noergaard's Infinity Series

Christopher Drexler-Lemire, Jeffrey Shallit

The Danish composer Per Noergaard defined the "infinity series" s = (s(n))_n>=0 by the rules s(0) = 0, s(2n) = -s(n) for n >= 1, and s(2n + 1) = s(n) + 1 for n >= 0; it figures pro…

math.CO2013

A Comprehensive Analysis of Polyhedral Lift-and-Project Methods

Yu Hin Au, Levent Tunçel

We consider lift-and-project methods for combinatorial optimization problems and focus mostly on those lift-and-project methods which generate polyhedral relaxations of the convex…

math.CO2009

Generalized de Bruijn words for Primitive words and Powers

Yu Hin Au

We show that for every $n \geq 1$ and over any finite alphabet, there is a word whose circular factors of length $n$ have a one-to-one correspondence with the set of primitive word…

math.CO2008

Van der Waerden's Theorem and Avoidability in Words

Yu-Hin Au, Aaron Robertson, Jeffrey Shallit

Pirillo and Varricchio, and independently, Halbeisen and Hungerbuhler considered the following problem, open since 1994: Does there exist an infinite word w over a finite subset of…

Enumerating Multi-Operator Monomials in Commutative and Noncommutative Settings

A new generalization of the Narayana numbers inspired by linear operators on associative d-ary algebras

A Computational Search for Minimal Obstruction Graphs for the Lovász--Schrijver SDP Hierarchy

Stable Set Polytopes with Rank ∣V(G)∣/3 for the Lovász--Schrijver SDP Operator

On Rank-Monotone Graph Operations and Minimal Obstruction Graphs for the Lovász--Schrijver SDP Hierarchy

Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operator

Decompositions of Unit Hypercubes and the Reversion of a Generalized Möbius Series

On Connections Between Association Schemes and Analyses of Polyhedral and Positive Semidefinite Lift-and-Project Relaxations

Some Properties and Combinatorial Implications of Weighted Small Schröder Numbers

Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube

Elementary polytopes with high lift-and-project ranks for strong positive semidefinite operators

Notes and Note-Pairs in Noergaard's Infinity Series

A Comprehensive Analysis of Polyhedral Lift-and-Project Methods

Generalized de Bruijn words for Primitive words and Powers

Van der Waerden's Theorem and Avoidability in Words

A new generalization of the Narayana numbers inspired by linear operators on associative $d$ -ary algebras

Stable Set Polytopes with Rank $∣ V (G) ∣/3$ for the Lovász--Schrijver SDP Operator