Séminaire Lotharingien de Combinatoire, B93b (2025), 15 pp.
Dimbiniaina Ratovilebamboavison, Mamy Laingo Nomenjanahary
Rakotoarison and Fanja Rakotondrajao
Factorial Euler-Seidel matrix: Refinement and q-analogue
Abstract.
We determine the Riordan matrix associated to Eulerian numbers and establish a formula defining Eulerian polynomials as well. We refine the factorial Euler-Seidel matrix considering the excedance distribution over permutations and derangements. We introduce the so called (n,k)-permutations. Combining with the number of cycles, we establish exponential generating functions and their q-analogues as well.
Received: June 18, 2025.
Revised: November 7, 2025.
Accepted: November 7, 2025.
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