J: How to effectively apply a verb to suffix prefixes?

Question

I have a list

   n =: i.3

and I want to be an adverb a , to uan applied u to the suffixes, prefixes n

   <a n
┌─────────────┬───────┬───┐
│┌─┬───┬─────┐│┌─┬───┐│┌─┐│
││0│0 1│0 1 2│││1│1 2│││2││
│└─┴───┴─────┘│└─┴───┘│└─┘│
└─────────────┴───────┴───┘

I wrote a sentence that gives the desired result for the verb < :

   ([: <@]\&.> <@]\.) n
┌─────────────┬───────┬───┐
│┌─┬───┬─────┐│┌─┬───┐│┌─┐│
││0│0 1│0 1 2│││1│1 2│││2││
│└─┴───┴─────┘│└─┴───┘│└─┘│
└─────────────┴───────┴───┘

but I cannot understand how to make an adverb to use it with any verb.

I see a different approach to this problem:

   a =: \\.
   <a n
┌─┬───┬─────┐
│0│0 1│0 1 2│
├─┼───┼─────┤
│1│1 2│     │
├─┼───┼─────┤
│2│   │     │
└─┴───┴─────┘
   ([: < (a: ~: ]) # ])"1(<a n)
┌─────────────┬───────┬───┐
│┌─┬───┬─────┐│┌─┬───┐│┌─┐│
││0│0 1│0 1 2│││1│1 2│││2││
│└─┴───┴─────┘│└─┴───┘│└─┘│
└─────────────┴───────┴───┘

but it is also written specifically for < and may be ineffective. And I still can’t understand how to make an adverb.

It will be even better if I get the following result:

   <a n
┌─┬───┬─────┬─┬───┬─┐
│0│0 1│0 1 2│1│1 2│2│
└─┴───┴─────┴─┴───┴─┘

For instance:

   (10&#.)a n
0 1 12 1 12 2

Help me please. Thanks in advance.

Answer 1

() . Spread (S:), 0.

.

<\ each <\. n
┌─────────────┬───────┬───┐
│┌─┬───┬─────┐│┌─┬───┐│┌─┐│
││0│0 1│0 1 2│││1│1 2│││2││
│└─┴───┴─────┘│└─┴───┘│└─┘│
└─────────────┴───────┴───┘
< S:0 <\ each <\. n
┌─┬───┬─────┬─┬───┬─┐
│0│0 1│0 1 2│1│1 2│2│
└─┴───┴─────┴─┴───┴─┘

+/ S:0 <\ each <\. n
0 1 3 1 3 2

(10&#.)  S:0 <\ each <\. n
0 1 12 1 12 2

, a :

a =: 1 :'u S: 0 ([: <\&.><\.) y'

() , @Tikkanz , S: :

a=: 1 : ';@([: u\&.> <@]\.)'

a=: 1 : ';@(<@(u\)\.)'