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$(p, q)$-analogues of the generalized Touchard polynomials and Stirling numbers

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Lahcen Oussi

Combinatorics · Submitted 24 Jun 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we introduce a $(p, q)$-deformed analogues of the generalized Touchard polynomials and Stirling numbers, the post-quantum analogues of the $q$-deformed generalized Touchard polynomials and Stirling numbers.

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arXiv ID2106.12935 (version 2)
Pith IDXALITYVT, Pith's permanent record of this paper and its review
CitationLahcen Oussi. "$(p, q)$-analogues of the generalized Touchard polynomials and Stirling numbers." arXiv:2106.12935 (2021). https://pith.science/paper/XALITYVT
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,023 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.04 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.60 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this paper we introduce a $(p, q)$-deformed analogues of the generalized Touchard polynomials and Stirling numbers, the post-quantum analogues of the $q$-deformed generalized Touchard polynomials and Stirling numbers. The connection between these deformations is established. A recurrence relation for the $(p, q)$-deformed generalized Touchard polynomials is expounded, elucidating a $(p, q)$-deformation of Spivey's relation.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we introduce a $(p, q)$-deformed analogues of the generalized Touchard polynomials and Stirling numbers, the post-quantum analogues of the $q$-deformed generalized Touchard polynomials and Stirling numbers. contribution 1.00 0.92 0.26 asserted 1.00
s1 The connection between these deformations is established. contribution 0.74 0.81 0.12 asserted 1.00
s2 A recurrence relation for the $(p, q)$-deformed generalized Touchard polynomials is expounded, elucidating a $(p, q)$-deformation of Spivey's relation. contribution 0.67 0.92 0.26 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we introduce a $(p, q)$-deformed analogues of the generalized Touchard polynomials and Stirling numbers, the post-quantum analogues of the $q$-deformed generalized Touchard polynomials and Stirling numbers. The connection between these deformations is established. A recurrence relation for the $(p, q)$-deformed generalized Touchard polynomials is expounded, elucidating a $(p, q)$-deformation of Spivey's relation.

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