The term "Partisan game" can refer to a couple of different contexts, so it would be helpful to clarify what specific aspect you're interested in. However, here are two primary interpretations: 1. **Political Context**: In the realm of politics, a "partisan game" refers to manipulative tactics or strategies employed by political parties or groups to gain an advantage over their opponents.

In game theory, a "star" typically refers to a specific type of network structure or game configuration, where one player (often referred to as the "central" or "hub" player) is directly connected to multiple other players (the "spokes" or "periphery" players), but those peripheral players are not directly connected to each other. This can be visualized as a star shape, with the central player at the center and the other players forming the points of the star.

Catherine Yan is a prominent figure in the field of finance and investment, particularly known for her role as a managing director and head of investment strategy and research at a leading financial institution. Notably, she has gained recognition for her insights on market trends, investment strategies, and economic analysis. In addition, Catherine Yan may also refer to specific individuals in various other domains such as academia, technology, or entertainment.

David Conlon may refer to multiple individuals, as it is not an uncommon name. However, one notable figure by that name is a mathematician known for his work in combinatorics and related areas. He has made significant contributions to various problems in mathematics, particularly in the field of Ramsey theory.

Emanuel Sperner was a German mathematician known primarily for his contributions to combinatorial mathematics, particularly in the fields of topology and set theory. Born on March 23, 1905, he developed several important concepts, including Sperner's theorem, which addresses the largest family of subsets of a finite set that can be chosen so that no one set is contained within another. His work has had a significant impact on both combinatorics and other areas of mathematics.

As of my last knowledge update in October 2023, Eugenia O'Reilly-Regueiro does not appear to be a widely recognized public figure, historical figure, or concept in mainstream discourse. It's possible that she is a private individual or a name that has come into prominence after my training cutoff.

Frank P. Ramsey (1903–1930) was a British mathematician, philosopher, and economist known for his contributions to various fields, including mathematics, logic, and decision theory. Despite his short life, he made significant advancements in several areas: 1. **Mathematics**: Ramsey is best known for his work in combinatorial mathematics. The Ramsey theory, which deals with conditions under which a certain order must appear in structures, is named after him.

John Riordan (1905–1982) was an American mathematician known for his work in combinatorics, generating functions, and number theory. He made significant contributions to the field, particularly in the areas of combinatorial methods and the study of special functions associated with mathematical sequences.

Imre Bárány is a Hungarian mathematician known for his work in combinatorics, particularly in areas related to convex geometry and discrete geometry. He has made significant contributions to various aspects of these fields, often focusing on the interplay between combinatorial structures and geometric properties.

James William Peter Hirschfeld does not appear to be a widely recognized public figure or concept based on the information available up to October 2023. It’s possible that he may be a private individual or a figure in a specific niche that is not broadly known.

Jennifer Morse is a notable mathematician recognized for her work in the areas of dynamical systems and topology. She has made significant contributions to the understanding of complex systems and the mathematical theories underlying them. Morse has also been involved in various academic and educational initiatives, promoting mathematics and supporting the mathematical community.

Lior Pachter is a prominent computational biologist known for his contributions to bioinformatics and systems biology. He is a professor at the California Institute of Technology (Caltech), where he works on problems at the intersection of biology, mathematics, and computer science. His research often focuses on developing algorithms and computational methods for analyzing biological data, such as genomic sequences, gene expression, and evolutionary patterns. Pachter is also known for his work in RNA sequencing analysis and statistical methods in genomics.

Miklós Simonovits is a Hungarian mathematician known for his contributions to various fields, particularly in combinatorics, graph theory, and number theory. He is recognized for his work on extremal combinatorial problems, including results related to the Erdős–Simonovits stability theorem. His research has had a significant influence on the development of combinatorial mathematics, and he has published numerous papers and contributed to many important theories in the field.

A "free lattice" typically refers to a type of lattice in the context of lattice theory, a branch of mathematics that studies ordered sets and their properties. In lattice theory, a lattice is a partially ordered set in which any two elements have a unique supremum (least upper bound, also known as join) and an infimum (greatest lower bound, or meet).

A cutting sequence, particularly in the context of mathematics and combinatorial optimization, refers to a specific arrangement or pattern of elements that allows for the division of a larger set into smaller, manageable subsets. While the term can apply to various fields, it is most commonly associated with graph theory, geometric constructions, and linear programming, where it may refer to processes involving partitioning objects or sequences into distinct parts.

In differential geometry and related fields, a **formally smooth map** generally refers to a type of map that behaves smoothly at a certain level, even if it may not be globally smooth in the traditional sense across its entire domain. The concept is often discussed in the context of algebraic geometry and singularity theory. To provide a clearer understanding: 1. **Smooth Maps**: A smooth map is typically a function between differentiable manifolds that is infinitely differentiable.

Hilbert's Basis Theorem is a fundamental result in algebra, particularly in the theory of rings and ideals. It states that if \( R \) is a Noetherian ring (meaning that every ideal in \( R \) is finitely generated), then any ideal in the polynomial ring \( R[x] \) (the ring of polynomials in one variable \( x \) with coefficients in \( R \)) is also finitely generated.

J-multiplicity is a concept that appears in the context of mathematical logic and model theory, particularly in the study of structures and their properties. It is often associated with the analysis of certain functions or relations over structures, and can be used to investigate how complex a particular model or theory is.