Q:

Is there a common mathematical symbology for collections? 

I am being asked to define several of my algorithms in mathematical terms to describe my work to a customer.   I am trying to determine if anybody knows whether common operators for collections like sequences, lists, tuples, etc have been defined.  If so, is there a good reference that I could be pointed to.  Thanks.  I am interested in the actual symbols used.   I am wondering if the following would make sense or be appropiate to anybody. 
Given two sequences (or strings):
S = (A, B, C) and T = (A, D, H)
In my mind, the intersection of these sequences would look like S ∩ T = (A) and the union of these sequences would be S ∪ T = (A, B, C, A, D, H)

A:

Sequences or lists in which there is an implied ordering of the elements are commonly delimited between 〈 and 〉. For example:
S = 〈A, B, C〉         (They look like <A, B, C>, but taller.  HTML entities are &lang; and &rang; )
If there is no order implied, use set notation. 
S = {A, B, C}
Tuples, such as rows from a table or ordered pairs/triples, use parentheses:
car = (Toyota, Camry, 2010)
coordinates = (10, 45)
The union and intersection of sets are represented with the ∪ and ∩ symbols, as usual. 
For lists, the operations are different.  You concatenate lists rather than finding their union.  This can be represented as S+T or simply ST (depending on who's watching). 
As tuples are indivisible, the union or intersection of two of them is nonsensical. 
You might want to ask this on https://cstheory.stackexchange.com/

