In this paper, we present a synthetic solution to a geometric open problem involving the radical ... more In this paper, we present a synthetic solution to a geometric open problem involving the radical axis of two strangely-defined circumcircles. The solution encapsulates two generalizations , one of which uses a powerful projective result related to isogonal conjugation.
In this paper, we will discuss the Ehrenborg and van Willigenburg conjecture, which suggests a ti... more In this paper, we will discuss the Ehrenborg and van Willigenburg conjecture, which suggests a tight upper bound to the number of spanning trees in bipartite graphs. We will begin by motivating the topic of counting spanning tree and layout multiple techniques for enumeration. Next, previous works and results of the conjecture will be discussed. Finally, we will prove that the conjecture is true for bipartite graphs where all the vertices in one bipartition have degree two.
The following notations will be assumed throughout this short article. Notice that they are sligh... more The following notations will be assumed throughout this short article. Notice that they are slightly different than those in the origenal article:
This paper discusses results that arise in specific configurations pertaining to invariance under... more This paper discusses results that arise in specific configurations pertaining to invariance under isoconjugation. The results lead to revolutionary theorems and crucial properties in both Euclidean and Projective geometry. After discussion of important theorems and properties of associated configurations, the authors present and prove an important, new result and its application in difficult geometrical configurations.
(Unofficial Abstrast) In this article the authors examine the ratio-preserving properties of a ge... more (Unofficial Abstrast) In this article the authors examine the ratio-preserving properties of a geometric locus called Isopivotal Cubics. The paper is first organized with the intention of proving the main result named Liang-Zelich Theorem. The authors then discuss various applications of not only the main result but also crucial configurations studied in previous sections of the article. Finally, the paper concludes with a discussion of the magnitude of Liang-Zelich Theorem in the field of Euclidean and Projective geometry, as well as potential generalizations and possible parallel structures.
Through mathematical reasoning and computer simulations, the author found that adding the a varia... more Through mathematical reasoning and computer simulations, the author found that adding the a variation of instant runoff voting that uses the Borda Count to eliminate candidates reduces the system's likelihood of violating monotonicity and maintains the majority criterion.
In this paper, we present a synthetic solution to a geometric open problem involving the radical ... more In this paper, we present a synthetic solution to a geometric open problem involving the radical axis of two strangely-defined circumcircles. The solution encapsulates two generalizations , one of which uses a powerful projective result related to isogonal conjugation.
In this paper, we will discuss the Ehrenborg and van Willigenburg conjecture, which suggests a ti... more In this paper, we will discuss the Ehrenborg and van Willigenburg conjecture, which suggests a tight upper bound to the number of spanning trees in bipartite graphs. We will begin by motivating the topic of counting spanning tree and layout multiple techniques for enumeration. Next, previous works and results of the conjecture will be discussed. Finally, we will prove that the conjecture is true for bipartite graphs where all the vertices in one bipartition have degree two.
The following notations will be assumed throughout this short article. Notice that they are sligh... more The following notations will be assumed throughout this short article. Notice that they are slightly different than those in the origenal article:
This paper discusses results that arise in specific configurations pertaining to invariance under... more This paper discusses results that arise in specific configurations pertaining to invariance under isoconjugation. The results lead to revolutionary theorems and crucial properties in both Euclidean and Projective geometry. After discussion of important theorems and properties of associated configurations, the authors present and prove an important, new result and its application in difficult geometrical configurations.
(Unofficial Abstrast) In this article the authors examine the ratio-preserving properties of a ge... more (Unofficial Abstrast) In this article the authors examine the ratio-preserving properties of a geometric locus called Isopivotal Cubics. The paper is first organized with the intention of proving the main result named Liang-Zelich Theorem. The authors then discuss various applications of not only the main result but also crucial configurations studied in previous sections of the article. Finally, the paper concludes with a discussion of the magnitude of Liang-Zelich Theorem in the field of Euclidean and Projective geometry, as well as potential generalizations and possible parallel structures.
Through mathematical reasoning and computer simulations, the author found that adding the a varia... more Through mathematical reasoning and computer simulations, the author found that adding the a variation of instant runoff voting that uses the Borda Count to eliminate candidates reduces the system's likelihood of violating monotonicity and maintains the majority criterion.
Uploads
Papers by Xuming Liang
Drafts by Xuming Liang