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July 2018 Associated binomial inversion for unified Stirling numbers and counting subspaces generated by subsets of a root system
Tomohiro Kamiyoshi, Makoto Nagura, Shin-ichi Otani
Tsukuba J. Math. 42(1): 97-125 (July 2018). DOI: 10.21099/tkbjm/1541559652

Abstract

We introduce an associated version of the binomial inversion for unified Stirling numbers defined by Hsu and Shiue. This naturally appears when we count the number of subspaces generated by subsets of a root system. We count such subspaces of any dimension by using associated unified Stirling numbers, and then we will also give a combinatorial interpretation of our inversion formula. In particular, the well-known explicit formula for classical Stirling numbers of the second kind can be understood as a special case of our formula.

Citation

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Tomohiro Kamiyoshi. Makoto Nagura. Shin-ichi Otani. "Associated binomial inversion for unified Stirling numbers and counting subspaces generated by subsets of a root system." Tsukuba J. Math. 42 (1) 97 - 125, July 2018. https://doi.org/10.21099/tkbjm/1541559652

Information

Received: 26 March 2018; Revised: 12 July 2018; Published: July 2018
First available in Project Euclid: 7 November 2018

zbMATH: 07055226
MathSciNet: MR3873533
Digital Object Identifier: 10.21099/tkbjm/1541559652

Subjects:
Primary: 11B73
Secondary: 05A15, 15A21, 17B22

Rights: Copyright © 2018 University of Tsukuba, Institute of Mathematics

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Vol.42 • No. 1 • July 2018
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