Timeline for Counting number of points in a lattice with bounded sup norm

11 events

when toggle format	what		by	license	comment
S Apr 19, 2015 at 3:09	history	bounty ended	SJY
S Apr 19, 2015 at 3:09	history	notice removed	SJY
S Apr 17, 2015 at 22:55	history	bounty started	SJY
S Apr 17, 2015 at 22:55	history	notice added	SJY		Reward existing answer
Apr 7, 2015 at 18:11	comment	added	Joe Silverman		Since you were asking about the $j$-volume of the parallelopiped $\mathcal P$ spanned by $v_1,\ldots,v_j$ in $\mathbb{R}^n$, you might find the following formula interesting. Let $A$ be the $n$-by-$j$ matrix the contains the vectors $v_1,\ldots,v_j$ as the columns. Let $B_1,B_2,\ldots,B_k$ denote all of the $j$-by-$j$ minors of $A$, so $k=\binom{n}{j}$. Then $\operatorname{Vol}(\mathcal P)^2 = \sum_{i=1}^k \det(B_i)^2$.
Apr 5, 2015 at 2:33	vote	accept	SJY
Apr 2, 2015 at 22:53	answer	added	GH from MO		timeline score: 4
Apr 2, 2015 at 17:57	history	edited	SJY	CC BY-SA 3.0	deleted 5 characters in body
S Apr 2, 2015 at 17:30	history	suggested	JustKevin	CC BY-SA 3.0	is that what you meant?
Apr 2, 2015 at 16:53	review	Suggested edits
S Apr 2, 2015 at 17:30
Apr 2, 2015 at 15:31	history	asked	SJY	CC BY-SA 3.0