Steven R. Lippold

activity

20212024

collaborators

6 papers

math.CO2024

Twin-star hypothesis and cycle-free $d$ -partitions of $K_{2 d}$

Matthew J. Fyfe, Steven R. Lippold, Mihai D. Staic +2

In this paper we study an equivalence relation defined on the set of cycle-free $d$ -partitions of the complete graph $K_{2 d}$ . We discuss a conjecture which states that this equiva…

math.RA2024

Permutation-Like Matrices

Steven Robert Lippold

Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on $d$ elements as a square $d \times d$ matrix. Motivated by [4], we define…

math.RA2023

The Algebra of $S^{2}$ -Upper Triangular Matrices

Steven R. Lippold

Based on work presented in [4], we define $S^{2}$ -Upper Triangular Matrices and $S^{2}$ -Lower Triangular Matrices, two special types of $d \times d (2 d - 1)$ matrices generalizing Upper an…

math.RA2022

Existence of the Map $d e t^{S^{3}}$

Steven R. Lippold, Mihai D. Staic

In this paper we show the existence of a nontrivial linear map $d e t^{S^{3}} : V_{d}^{\otimes (3 3 d)} \to k$ with the property that $det^{S^3}(\otimes_{1\leq i<j<k\leq 3d}(v_{i,j,k})…

math.CO2021

Partitions of the complete hypergraph $K_{6}^{3}$ and a determinant like function

Steven R. Lippold, Mihai D. Staic

In this paper we introduce a determinant-like map $d e t^{S^{3}}$ and study some of its properties. For this we define a graded vector space $Λ_{V}^{S^{3}}$ that has similar properties wit…

math.CO2021

Edge partitions of the complete graph and a determinant like function

Steven R. Lippold, Mihai D. Staic, Alin Stancu

In this paper we prove the case $d im (V_{3}) = 3$ of a conjecture about the exterior operad $Λ_{V_{d}}^{S^{2}}$ . For this we introduce a collection of natural involutions on the set of homo…

Twin-star hypothesis and cycle-free d-partitions of K2d​

Permutation-Like Matrices

The Algebra of S2-Upper Triangular Matrices

Existence of the Map detS3

Partitions of the complete hypergraph K63​ and a determinant like function

Edge partitions of the complete graph and a determinant like function

Twin-star hypothesis and cycle-free $d$ -partitions of $K_{2 d}$

The Algebra of $S^{2}$ -Upper Triangular Matrices

Existence of the Map $d e t^{S^{3}}$

Partitions of the complete hypergraph $K_{6}^{3}$ and a determinant like function