Timeline for Recurrent relation with several indices ( How many $m$-dim cubes in $n$-dim cube )

10 events

when toggle format	what		by	license	comment
Oct 11, 2017 at 15:40	history	edited	LRDPRDX	CC BY-SA 3.0	added 9 characters in body
Mar 8, 2017 at 13:32	history	edited	LRDPRDX	CC BY-SA 3.0	deleted 18 characters in body
Mar 7, 2017 at 9:38	history	edited	LRDPRDX	CC BY-SA 3.0	edited title
Mar 7, 2017 at 9:35	comment	added	LRDPRDX		My solution in the context of $n$-dim cube is the following. Obviously, that there are $2^n$ vertices in $n$-dim cube. Then at each vertex choose $m$ $1$-dim edges which are part of $m$-dim cube. You will obtain $2^n C_{n}^{m}$. But you should divide this number by the number of how many times the same $m$ -dim cube was added in total sum which is $2^m$. Voilà, $Q_{n}^{m} = 2^{n-m}C_{n}^{m}.$
Mar 6, 2017 at 16:43	history	edited	LRDPRDX	CC BY-SA 3.0	added 75 characters in body
Mar 6, 2017 at 16:35	vote	accept	LRDPRDX
Mar 6, 2017 at 10:12	history	edited	LRDPRDX	CC BY-SA 3.0	deleted 2 characters in body
Mar 6, 2017 at 9:54	answer	added	T. Amdeberhan		timeline score: 4
Mar 6, 2017 at 9:35	comment	added	Dima Pasechnik		typically one would use a multivariate generating function for these kinds of problems.
Mar 6, 2017 at 8:30	history	asked	LRDPRDX	CC BY-SA 3.0