EXPLORING THE VOLUME POLYNOMIAL AND M-CONVEXITY IN MATROID THEORY
EXPLORING THE VOLUME POLYNOMIAL AND M-CONVEXITY IN MATROID THEORY
Tushar Pradip Atole(University of Technology and Applied Science); Namrata Kaushal(독립연구자); Jyoti Gupta(Indore Institute of Science and Technology)
43권 1호, 179~189쪽
초록
This study explores the diverse functions of volume polynomials in encoding graded Poincare duality algebras and matroid theory. Volume polynomials play a key role in algebraic geometry by measuring degrees of ample divisors and offer a combinatorial perspective on transversals in bipartite graphs through the dragon marriage theorem. The research confirms that volume polynomials maintain their properties under multiplication and linear transformations and establishes their Lorentzian property in matroid theory. Additionally, it revisits the Hall-Rado formula to provide new insights into combinatorial structures. Overall, this study enhances our understanding of how algebraic, combinatorial, and geometric models interact, highlighting the unifying role of volume polynomials across various mathematical domains.
Abstract
This study explores the diverse functions of volume polynomials in encoding graded Poincare duality algebras and matroid theory. Volume polynomials play a key role in algebraic geometry by measuring degrees of ample divisors and offer a combinatorial perspective on transversals in bipartite graphs through the dragon marriage theorem. The research confirms that volume polynomials maintain their properties under multiplication and linear transformations and establishes their Lorentzian property in matroid theory. Additionally, it revisits the Hall-Rado formula to provide new insights into combinatorial structures. Overall, this study enhances our understanding of how algebraic, combinatorial, and geometric models interact, highlighting the unifying role of volume polynomials across various mathematical domains.
- 발행기관:
- 한국전산응용수학회
- 분류:
- 수학