Tsukuba Journal of Mathematics

Associated binomial inversion for unified Stirling numbers and counting subspaces generated by subsets of a root system

Tomohiro Kamiyoshi, Makoto Nagura, and Shin-ichi Otani

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Tsukuba J. Math., Volume 42, Number 1 (2018), 97-125.

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

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1541559652

Digital Object Identifier
doi:10.21099/tkbjm/1541559652

Mathematical Reviews number (MathSciNet)
MR3873533

Zentralblatt MATH identifier
07055226

Subjects
Primary: 11B73: Bell and Stirling numbers
Secondary: 17B22: Root systems 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 15A21: Canonical forms, reductions, classification

Keywords
associated binomial inversion unified Stirling number root system

Citation

Kamiyoshi, Tomohiro; Nagura, Makoto; Otani, Shin-ichi. Associated binomial inversion for unified Stirling numbers and counting subspaces generated by subsets of a root system. Tsukuba J. Math. 42 (2018), no. 1, 97--125. doi:10.21099/tkbjm/1541559652. https://projecteuclid.org/euclid.tkbjm/1541559652


Export citation