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Bibliographic Details
Main Authors: Konvalinka, Matjaž, Petersen, T. Kyle
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.19076
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Table of Contents:
  • The Eulerian numbers form a triangular array with many interesting properties. The numbers arise from various combinatorial and probabilistic interpretations, and have been studied in a variety of mathematical contexts. In this article we examine two distinct alternating sign formulas for the Eulerian numbers and show how they can be proved using a sign-reversing involution technique described by Benjamin and Quinn known as the ``D.I.E.'' method. Each of these arguments lends itself to a broad generalization, shedding light on different parts of mathematics.