Y. Au

activity

20242026

collaborators

7 papers

math.CO2026

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

Yu Hin Au, Levent TunÃ§el

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

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.CO2026

A Computational Search for Minimal Obstruction Graphs for the LovÃ¡sz--Schrijver SDP Hierarchy

Yu Hin Au, Levent TunÃ§el

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 LovÃ¡sz and Schrijver. Our f…

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

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.CO2025

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

Yu Hin Au, Nathan Lindzey, Levent TunÃ§el

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

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

Enumerating Multi-Operator Monomials in Commutative and Noncommutative Settings

A Computational Search for Minimal Obstruction Graphs for the LovÃ¡sz--Schrijver SDP Hierarchy

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

Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube

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

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

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