We exhibit a connection between two statistics on set partitions, the intertwining number and the depth-index. In particular, results link the intertwining number to the algebraic geometry of Borel orbits. Furthermore, by studying the generating polynomials of our statistics, we determine the $q=-1$ specialization of a $q$-analogue of the Bell numbers. Finally, by using Renner's $H$-polynomial of an algebraic monoid, we introduce and study a $t$-analog of $q$-Stirling numbers.
@article{10_37236_7986,
author = {Mahir Bilen Can and Yonah Cherniavsky and Martin Rubey},
title = {A geometric interpretation of the intertwining number},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {2},
doi = {10.37236/7986},
zbl = {1409.05027},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7986/}
}
TY - JOUR
AU - Mahir Bilen Can
AU - Yonah Cherniavsky
AU - Martin Rubey
TI - A geometric interpretation of the intertwining number
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/7986/
DO - 10.37236/7986
ID - 10_37236_7986
ER -
%0 Journal Article
%A Mahir Bilen Can
%A Yonah Cherniavsky
%A Martin Rubey
%T A geometric interpretation of the intertwining number
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/7986/
%R 10.37236/7986
%F 10_37236_7986
Mahir Bilen Can; Yonah Cherniavsky; Martin Rubey. A geometric interpretation of the intertwining number. The electronic journal of combinatorics, Tome 26 (2019) no. 2. doi: 10.37236/7986
