**4. Conclusions**

In our previous paper [4], we studied some identities of symmetry on the Carlitz-type degenerate (*p*, *q*)-Euler polynomials. The motivation of this paper is to investigate some explicit identities for the Carlitz-type higher-order degenerate (*p*, *q*)-Euler polynomials in the second row of the diagram at page 3. Thus, we defined the Carlitz-type higher-order degenerate (*p*, *q*)-Euler polynomials in Definition 2 and obtained the formulas (explicit formula (Theorem 6), multiplication theorem (Theorem 8), and distribution relation (Corollary 2, Corollary 3)). In Theorem 7, we gave some symmetry identities for the Carlitz-type higher-order degenerate (*p*, *q*)-Euler polynomials. We also obtained the explicit identities related to the Carlitz-type higher-order (*p*, *q*)-Euler polynomials, the alternating (*p*, *q*)-sums of powers, and Stirling numbers (see Theorem 10 and Corollary 4). In particular, these results generalized some well-known properties relating degenerate Euler numbers and polynomials, degenerate Stirling numbers, alternating sums of powers, multiplication theorem, distribution relation, falling factorial, symmetry properties of the degenerate Euler numbers and polynomials (see [7–18]). In addition, in this paper, if we take *r* = 1, then [4] is the special case of this paper.

**Author Contributions:** These authors contributed equally to this work.

**Funding:** This work was supported by the Dong-A university research fund.

**Acknowledgments:** The authors would like to thank the referees for their valuable comments, which improved the original manuscript in its present form.

**Conflicts of Interest:** The authors declare no conflicts of interest.
