2021/11/22 by Sirous Homayouni, Homayouni, Sirous
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.2111.10982
25 pages, 2 diagrams, 1 table
arxiv created 2021/11/22 · openalex publication_date 2021/11/22 · arxiv updated 2021/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a quotient of Fomin-Kirillov algebra FK(n) denoted FKCn(n), over the ideal generated by the edges of a complete graph on n vertexes that are missing in the n-cycle graph Cn. For this quotient algebra FKCn(n), we show that the basis is in one-to-one correspondence with the set of matchings in an n-cycle graph. We also prove that the dimension of FKCn(n) equals the Lucas Number Ln and its Hilbert series is q-Lucas polynomial. We find the character map of this quotient algebra over Dihedral group Dn.