Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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EXPLORING THE VOLUME POLYNOMIAL AND M-CONVEXITY IN MATROID THEORY

  • TUSHAR ATOLE (Faculty of Department of Mathematics, University of Technology and Applied Science) ;
  • NAMRATA KAUSHAL (Faculty of Department of Mathematics, Indore Institute of Science and Technology) ;
  • JYOTI GUPTA (Faculty of Department of Mathematics, Indore Institute of Science and Technology)
  • Received : 2024.09.02
  • Accepted : 2024.12.07
  • Published : 2025.01.30
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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.

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Acknowledgement

We are extremely grateful to all those who played a role in the success of this research work. We would like to express our gratitude towards the management for the encouragement and all the supporting staff for their invaluable input and support throughout the research process.

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