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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