Lucas aggregate supply function: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>EdJohnston
→See also: Lucas islands model -- target has moved per WP:RM
 
Line 1: Line 1:
In [[mathematics]] (and particularly in [[combinatorics]]), the '''major index''' of a [[permutation]] is defined as the sum of the positions of the [[Permutation#Ascents, descents and runs|descents]] of the permutation. In symbols, the major index of the permutation ''w'' is
<br><br>If you happen to be searching for a [http://Ziatina4Ever.Altervista.org/userinfo.php?uid=28714 single tool] that will meet a number of requirements whilst taking up much less space in your tool box or backpack than person tools, you might want to contemplate a multi tool. These Gerber multi tool testimonials will help you decide which one will be most effective for you.<br><br>And, not surprisingly, the tool looks really good. Jay from CopTool has a great critique up at his web site that puts the tool head to head with the Fein. So this a single was just a matter of time. We're actually [http://mynewfriendz.com/biding/item.php?id=39659&mode=1 shocked] it took so long for Milwaukee to get with the [http://69.89.27.245/~kickbox6/socialecorner/groups/where-to-buy-a-machete/ oscillating tool] plan and on top of that, we're basically disappointed that they opted for a cordless version. We privately had high hopes for a corded version that would give King Fein some competitors. No such luck. It looks like this oscillating tool has all of the trappings of yet an additional strong Milwaukee offering a metal gear case, a nice gripping location, and simple controls. The kit comes with two batteries and an accessory adapter which makes it compatible with most available accessories.<br><br>I used to cart my leatherman around all the time and [http://wiki.myriadtalk.com/index.php?title=Best_Bolo_Machete ultimately stopped] when I realized most of the time I necessary to reduce something and I frequently made use of a modest pocket knife for that. I have owned each Leatherman tools and Gerber tools. The Gerber ones are DEFINATELY inferior to the Leatherman ones. Gerber doesn't make pretty fantastic knives in basic. They use soft, inferior grade steels. I picked up a Leatherman Core yesterday and am happy with it. I bought it particularly for the reason that it did NOT have a pair of scissors which I see as a waste of space and weight. I also like that the tools and blades lock open. a two.9-inch 420HC knife (HC stands for “high carbon,” which implies the knife will hold an edge superior) Keychain carry of the tiny and burly Leatherman PS4.<br><br>Its not also loud, not to heavy, utilizing it with no the supplied strap now. I believe the engine may have to have a tweak to get the most effective out of it. Tools do transform but can be fiddly to get inserted suitable just about every time. The stainless steel handles on the SOG B66N-CP supply comfort when doing the toughest duties. Even though this multi-tool features gear covers and hex bolts it is lightweight and portable with dimensions of just 5.five x 1.6 x 2. If you have any kind of questions pertaining to where and exactly how to utilize [http://Www.thebestpocketknifereviews.com/best-survival-machete-on-the-market-today/ best survival machete], you can call us at our site. 9 inches. As with other SOG items, the SOG B66N-CP multi-tool is backed by a lifetime warranty that protects it against defects in manufacturing and supplies. Item Description When equipped with a narrow blade, a multi-tool can make plunge cuts in boards, flooring or drywall.
 
: <math>
\operatorname{maj}(w) = \sum_{w(i)>w(i+1)} i.
</math>
 
For example, if ''w'' is given in [[Permutation#Notation|one-line notation]] by ''w'' = 351624 (that is, ''w'' is the permutation of {1, 2, 3, 4, 5, 6} such that ''w''(1) = 3, ''w''(2) = 5, etc.) then ''w'' has descents at positions 2 (from 5 to 1) and 4 (from 6 to 2) and so maj(''w'') = 2 + 4 = 6.
 
This [[permutation statistic|statistic]] is named after [[Percy Alexander MacMahon|Major Percy Alexander MacMahon]] who showed in [[#CITEREFMacMahon1913|1913]] that the distribution of the major index on all permutations of a fixed length is the same as the distribution of [[Permutation#Inversions|inversions]]. That is, the number of permutations of length ''n'' with ''k'' inversions is the same as the number of permutations of length ''n'' with major index equal to ''k''. (These numbers are known as ''Mahonian numbers'', also in honor of MacMahon.<ref>M. Bóna, Combinatorics of Permutations, 2004, p. 43ff, ISBN 1-58488-434-7.</ref>)  In fact, a stronger result is true: the number of permutations of length ''n'' with major index ''k'' and ''i'' inversions is the same as the number of permutations of length ''n'' with major index ''i'' and ''k'' inversions, that is, the two statistics are equidistributed.  For example, the number of permutations of length 4 with given major index and number of inversions is given in the table below.
:<math>\begin{array}{c|ccccccc}
& 0&1&2&3&4&5&6 \\
\hline
0&1&0&0&0&0&0&0 \\
1&0&1&1&1&0&0&0 \\
2&0&1&2&1&1&0&0 \\
3&0&1&1&2&1&1&0 \\
4&0&0&1&1&2&1&0 \\
5&0&0&0&1&1&1&0 \\
6&0&0&0&0&0&0&1
\end{array}
</math>
== References ==
<references />
*{{Cite journal
| last1=MacMahon | first1=P. A. | author1-link=Percy Alexander MacMahon
| title=The indices of permutations and the derivation therefrom of functions of a single variable associated with the permutations of any assemblage of objects
| year=1913
| journal=Amer. J. Math.
| volume=35
| number=3
| pages=281&ndash;322
| jstor=2370312}}.
 
{{DEFAULTSORT:Major Index}}
[[Category:Permutations]]
 
{{combin-stub}}

Latest revision as of 17:36, 28 July 2014



If you happen to be searching for a single tool that will meet a number of requirements whilst taking up much less space in your tool box or backpack than person tools, you might want to contemplate a multi tool. These Gerber multi tool testimonials will help you decide which one will be most effective for you.

And, not surprisingly, the tool looks really good. Jay from CopTool has a great critique up at his web site that puts the tool head to head with the Fein. So this a single was just a matter of time. We're actually shocked it took so long for Milwaukee to get with the oscillating tool plan and on top of that, we're basically disappointed that they opted for a cordless version. We privately had high hopes for a corded version that would give King Fein some competitors. No such luck. It looks like this oscillating tool has all of the trappings of yet an additional strong Milwaukee offering a metal gear case, a nice gripping location, and simple controls. The kit comes with two batteries and an accessory adapter which makes it compatible with most available accessories.

I used to cart my leatherman around all the time and ultimately stopped when I realized most of the time I necessary to reduce something and I frequently made use of a modest pocket knife for that. I have owned each Leatherman tools and Gerber tools. The Gerber ones are DEFINATELY inferior to the Leatherman ones. Gerber doesn't make pretty fantastic knives in basic. They use soft, inferior grade steels. I picked up a Leatherman Core yesterday and am happy with it. I bought it particularly for the reason that it did NOT have a pair of scissors which I see as a waste of space and weight. I also like that the tools and blades lock open. a two.9-inch 420HC knife (HC stands for “high carbon,” which implies the knife will hold an edge superior) Keychain carry of the tiny and burly Leatherman PS4.

Its not also loud, not to heavy, utilizing it with no the supplied strap now. I believe the engine may have to have a tweak to get the most effective out of it. Tools do transform but can be fiddly to get inserted suitable just about every time. The stainless steel handles on the SOG B66N-CP supply comfort when doing the toughest duties. Even though this multi-tool features gear covers and hex bolts it is lightweight and portable with dimensions of just 5.five x 1.6 x 2. If you have any kind of questions pertaining to where and exactly how to utilize best survival machete, you can call us at our site. 9 inches. As with other SOG items, the SOG B66N-CP multi-tool is backed by a lifetime warranty that protects it against defects in manufacturing and supplies. Item Description When equipped with a narrow blade, a multi-tool can make plunge cuts in boards, flooring or drywall.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Lucas_aggregate_supply_function&oldid=267087"