co.combinatorics – Proof of sign reversal of the tree inversion generating function at $ -1 $ is equal to the number of alternate permutations?

For a labeled tree $ T $ sure $ {1,2, …, n } $ a inversion of $ T $ is a pair $ 1 <i <j leq n $ such as $ j belongs to the unique path of $ 1 $ at $ i $ (we think of $ T $ as being rooted in $ 1 $). Let $ mathrm {inv} (T) $ indicate the number of inversions of $ T $.

Define the generating function $ f (q): = sum_ {T} q ^ { mathrm {inv} (T)} $ where the sum is on all the trees labeled on $ {1,2, …, n } $.

So we know that $ f (-1) $ is the number of alternate permutations in $ mathfrak {S} _n $ (that is to say the so-called "Euler number"). See, for example, Goulden-Jackson 3.3.49 (d).

Question: Is there a simple proof of this result via inversion inversion of sign?

android – Do I need help generating a QR code?

enter the description of the image hereI know it is easy, but in the way that I learned, nothing works for me. My PHP code is as follows:

How to generate the QR code at the time of registration of the product with all its data? Please help me, I am desperate.

mysql – What is the best solution for storing data and generating graphics?

I'm working on a project that will look like a discussion forum. However, in addition to creating the subject, the user must answer a 40-question quiz. These questions will be stored and subsequently displayed in graphs with the statistical results of all the users who answered the questionnaire.

My question is: Would mysql be a good choice for this project?

Over time, as the number of responses increases, would calculating and displaying graphs become too slow?

What is the best way for me not to have speed problems in the future?

I can not access the target device by generating a payload in metasploit

I am a beginner in Kali Linux,
after generating a load, there is this command (an interface can be specified) after the listening address. why is it happening

seo – Google can not retrieve a large sitemap containing 50,000 URLs, or browsers generating it

My sitemap contains 50,000 URLs / 7.8 MB and the following URL syntax:, maquiagem,   2019-10-03T17:12:01-03:00 

The problems are:

• The search console indicates that "The site map could not be read".

• Loading the Sitemap takes 1 hour and Chrome stops working.

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• In Firefox, the Sitemap downloaded in 1483ms and fully loaded after 5 minutes);

Things I did without success:

• disable GZip compression;

• Delete my .htaccess file;

• Create a Test Sitemap with 1 KB URLs and the same syntax that you sent to the Search Console. It worked, but the Sitemap of 50,000 URLs still indicates "" the inability to retrieve the Sitemap ";

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• I tried to inspect the URL directly, but this gave an error and asked to try again later while the 1K URL was working;

• I tried to validate the Sitemap on five different sites (YANDEX, ETC) and all worked without error or warning.

A light?

visualization – Generating ensemble partition diagrams

I recently came across a very nice illustration of game scores on wikipedia (Partition of a game article)

I need something similar but suited to my case (I need game scores of 4, but use different styles for the balls two and down), someone who was there a good start code for this?

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General method for generating d {d1, d2, d3 … dn} in AnyDice

I'm trying to find a more general method to create some one-sided distributions with the help of, such that values ​​less than or equal to 0 are displayed as 0 and the rest, normally , from a 2dy-8 dice roll.

For example, for a 2d6-8, I will enter the following:

output (2d6-8>0)*d{d1,d2,d3,d4},

while for 2d7-8, I will enter the following:

output (2d7-8>0)*d{d1,d2,d3,d4,d5,d6}.

These give me exactly what I want, but for higher values ​​of y (2d12, for example), it gets heavier. So I wonder if there is a more general (compact) way of writing it. Moreover, I do not want to have to create a custom function, but rather to use only the general language in a line "output xxx" used by anydice.

Any help or suggestion is greatly appreciated.

magento 1.9 – Magento1 in the administrator while generating the total of the paid bill becomes double the grand total

I have just faced a very strange problem in Magento 1 store, please look at it if you have ever faced this type of problem.

My Magento shop uses the Razorpay extension and when the customer places the order, it works perfectly on the front end and indicates the appropriate amount in the total order.

details of the order

But when I generate the bill, the total paid becomes double the grand total, see screen capture below.

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After some research, I go to the file below:

app code core Mage Sales Model Order Invoice.php

On the line number: 422, I see that they are settled on the total paid by adding the grand total and the total paid, please check the screenshot below.

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In addition, when placing the order by the customer via the Razorpay payment method, I see a code on which, if the status becomes a success, the extension defines the total amount paid and the total amount paid. If I comment on these codes, in the totals section of the order, this amount appears in Total due instead of Total paid.

So, please let me know if you are facing this type of error before.

Magento2 Redis generating sessions without visitors

I've added the redis server to store the sessions.
However, after adding redis, it seems that the speed is slower. Loader on the product page takes longer now.
In addition, I opened redis-cli monitor to check sessions and found that it generated sessions without any activity on the front-end. There is no visitor and no page is open.
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Is Reddit good for generating traffic? Yes? Then how?

Everyone tells me what is the right way to use Reddit and how we can drive traffic to my website.