2007/03/07 by Matjaž Konvalinka, Konvalinka, Matjaž · 7 citations
Chemistry · Mathematics · #05A15 #15A09 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Chemistry #Combinatorics (math.CO) #FOS: Mathematics #Generalization #Mathematical analysis #Mathematics #Pure mathematics #Transformation (genetics) #math.CO #msc:05A15 #msc:15A09
paper · pdf · doi:10.48550/arxiv.math/0703203
published in arXiv (Cornell University) (Cornell University) · 17 pages, 8 figures
arxiv created 2007/03/07 · openalex publication_date 2007/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The right-quantum algebra was introduced recently by Garoufalidis, Lê and Zeilberger in their quantum generalization of the MacMahon master theorem. A combinatorial proof of this identity due to Konvalinka and Pak, and also the recent proof of the right-quantum Sylvester's determinant identity, make heavy use of a bijection related to the first fundamental transformation on words introduced by Foata. This paper makes explicit the connection between this transformation and right-quantum linear algebra identities; applications include a new combinatorial proof of the right-quantum matrix inverse theorem, and two new results, the right-quantum Jacobi ratio theorem and a generalization of the right-quantum MacMahon master thorem.