Tsukuba Journal of Mathematics
- Tsukuba J. Math.
- Volume 42, Number 1 (2018), 97-125.
Associated binomial inversion for unified Stirling numbers and counting subspaces generated by subsets of a root system
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.
Tsukuba J. Math., Volume 42, Number 1 (2018), 97-125.
Received: 26 March 2018
Revised: 12 July 2018
First available in Project Euclid: 7 November 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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