elementary set theory – Notation for set containing combinations of sets given by multinomial coefficient number of options.

Assume there are sets $A_1,A_2,dots,A_n$. Let $mleq n$ and now partition ${1,dots,n}$ into $m$ subsets $N_1,dots,N_m$. So, there are basically
$$sum_{l_1+dots+l_m = n} {{n}choose{l_1,dots,l_m}}$$
different ways to do this.
$$B_i = bigcap_{iin N_i} A_i cap bigcap_{iin{1,dots,n}setminus N_i} A_i^c.$$
I am interested in the set containing ${B_1,dots,B_m}$ for all possible partitions of ${1,dots,n}$ into $m$ sets. So something like
$$C={{B_1,dots,B_m} | N_1,dots,N_m text{ partition of }{1,dots,n} text{ and } B_i text{ chosen as above}}.$$
Is there are more elegant way to define this $C$?

8 – How to build custom options for sections in layout builder?

As per title, I manage to build/define some custom blocks with my own parameters/form elements when placing them, so I’m looking to do the same with sections. I’ve seen that the core code does that, but ideally I would like to add more form elements to that interface and allow the editors to customise a bit more the abilities of each section. I found the core file that contains the functions but doesn’t feel right to me to just copy the whole file and modify it for my purpose.

So, what I’m looking is the proper way to do it, any documentation would help or a certain methodology you guys usually use.

wi fi – Wifi WPA Enterprise – In android 11 under ‘Online Certificate Status’, what is the difference between the various options?

Recently I noticed that my Note 10 would no longer associate with my wifi but all other phones would. I have since resolved the issue by rerolling my certificates but cannot get the options ‘Require status for all certificates’ or ‘Require status for untrusted certificates’ to work. ‘Request Status’ does work as well as ‘Don’t validate’

‘Require status for all certificates’ fails with on the freeradius end with –

(36) eap: Expiring EAP session with state 0xb8be52eabb005f50
(36) eap: Finished EAP session with state 0xb8be52eabb005f50
(36) eap: Previous EAP request found for state 0xb8be52eabb005f50, released from the list
(36) eap: Peer sent packet with method EAP TLS (13)
(36) eap: Calling submodule eap_tls to process data
(36) eap_tls: Continuing EAP-TLS
(36) eap_tls: (eaptls verify) = ok
(36) eap_tls: Done initial handshake
(36) eap_tls: <<< recv TLS 1.1 (length 0002)
(36) eap_tls: ERROR: TLS Alert read:fatal:internal error
(36) eap_tls: TLS_accept: Need to read more data: error
(36) eap_tls: ERROR: Failed in FUNCTION (SSL_read): error:14094438:SSL routines:ssl3_read_bytes:tlsv1 alert internal error
(36) eap_tls: TLS – In Handshake Phase
(36) eap_tls: TLS – Application data.
(36) eap_tls: ERROR: TLS failed during operation
(36) eap_tls: ERROR: (eaptls process) = fail
(36) eap: ERROR: Failed continuing EAP TLS (13) session. EAP sub-module failed
(36) eap: Sending EAP Failure (code 4) ID 190 length 4

‘Require status for untrusted’ hangs with android eventually giving up with this on the freeradius end –

(5) eap_tls: (eaptls start) = request
(5) eap: Sending EAP Request (code 1) ID 243 length 6
(5) eap: EAP session adding &reply:State = 0xcff1ecc3cf02e118
(5) (eap) = handled
(5) } # authenticate = handled
(5) Using Post-Auth-Type Challenge
(5) Post-Auth-Type sub-section not found. Ignoring.
(5) # Executing group from file /etc/raddb/sites-enabled/default
(5) Sent Access-Challenge Id 247 from to length 0
(5) EAP-Message = 0x01f300060d20
(5) Message-Authenticator = 0x00000000000000000000000000000000
(5) State = 0xcff1ecc3cf02e118ed54fc1c4b664912
(5) Finished request
Waking up in 4.9 seconds.
(5) Cleaning up request packet ID 247 with timestamp +19
Ready to process requests

What do I need to implement or correct so these two options will work as well?

bluetooth – Options for Integrating or developing a physical security solution (physical access control via in-house mobile apps [NFC/Bluetooh])

Our team is looking to either integrate or develop a physical security solution for a rather large campus.


Ability to either integrate (with reader/electronic lock hardware) from our mobile apps which would allow access control (over NFC/Bluetooth) to areas.

We will be writing to our already existing identity management api’s and expanding them to support what we need to for this project.

We are looking to write our own mobile integrations with purchased hardware, since this functionality has to exist within our organization’s already existing mobile apps we developed. (we haven’t found a company that offers the level of integration we want… most of the solutions we see out there are fantastic, but require downloading the security company’s mobile app, managing access control via their cloud resources, etc).

What reader/electronic door lock hardware can we buy to build this level of in-house integration with?

To summarize: we are looking to buy scanners/door locks with NFC/Bluetooth capability and write security integrations for access control through already existing mobile apps we have developed…

I realize product suggestions can be of bad taste on here, but I invite them for the sake of discussion in addition to solutions that companies offer.

Our team will be expanding to hire security professionals in this realm to assist, so you can save the “don’t roll your own auth” type of answers and comments 🙂

Thanks in advance!