Perfect Matchings on Width-3 Klein Bottle Grid Graphs
Year: 2026
Type: preprint
Abstract: Let K_{3,2n} be the multigraph obtained from the 3 x 2n square grid by cyclic identification in the length direction and a Mobius twist in the width direction. We enumerate perfect matchings of K_{3,2n}. Using a transfer-matrix reduction, we obtain the generating function A(x) = sum_{n>=1} a_n x^n = 2x(8 + 9x - 40x^2 - 27x^3 + 22x^4 + 4x^5) / ((1 + 2x - x^2)(1 - 6x - 3x^2 + 6x^3 + x^4)) and the order-six recurrence a_n = 4a_{n-1} + 16a_{n-2} - 6a_{n-3} - 16a_{n-4} + 4a_{n-5} + a_{n-6}, with initial values a_1 = 16, a_2 = 82, a_3 = 504, a_4 = 3178, a_5 = 20072, a_6 = 126872. The dominant growth rate is lambda = (3 + sqrt(10) + sqrt(23 + 6 sqrt(10))) / 2 approx 6.32049. The sequence is recorded in the OEIS as A398567.
Author: Muller, Jean Lauro
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204461323
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