My spreadsheet contains information about companies and is structured ledger-like in this way:

Company   Quarter   Revenues   EBITDA
A         2010.1    5          1
A         2010.2    6          1
B         2010.1    10         2
B         2010.2    12         3
B         2010.3    20         5
A         2010.3    8          2
B         2011.1    14         3
A         2010.3    8          2
A         2010.4    7          2
A         2011.1    9          1

I want:

• a formula (not GAS) that will show me a list of duplicates for the combination Company-Quarter. In the above example, there are two entries for Company A for Quarter 2010.3. In the data there could be multiple duplicates.

• a formula (not GAS) that give me missing Company-quarters for a given quarters range for all companies that have at least one entry in the date range (or alternatively, from a pre-determined list of Companies). In the above example, for the range 2010.1 to 2011.1, there is no entry for Company B in 2010.4. In the data there could be multiple missing information.

Ideally, I won't need to create auxiliary columns and is all contained in one formula, so as to make the spreadsheet more elegant.

— xxx —

Thanks to @Tedinoz answer below, I came down to a one-cell formula, copied here for future reference:
=unique(sort(arrayformula(if(arrayformula(isna(vlookup(unique(arrayformula(transpose(split(join("", arrayformula(rept(filter(UNIQUE(A2:A), len(UNIQUE(A2:A)))&char(9999), counta(transpose(split(join("", arrayformula(rept(filter(arrayformula(unique(mid(query(B2:B),1,4))), len(arrayformula(unique(mid(query(B2:B),1,4)))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),6,1))))))), char(9999))) )))), char(9999))) &" "&transpose(split(rept(join(char(9999), filter(arrayformula((transpose(split(join("", arrayformula(rept(filter(arrayformula(unique(mid(query(B2:B),1,4))), len(arrayformula(unique(mid(query(B2:B),1,4)))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),6,1))))))), char(9999))) )&"."&(transpose(split(rept(join(char(9999), filter(arrayformula(unique(mid(query(B2:B),6,1))), len(arrayformula(unique(mid(query(B2:B),6,1))))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),1,4))))), char(9999))))), len(arrayformula((transpose(split(join("", arrayformula(rept(filter(arrayformula(unique(mid(query(B2:B),1,4))), len(arrayformula(unique(mid(query(B2:B),1,4)))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),6,1))))))), char(9999))) )&"."&(transpose(split(rept(join(char(9999), filter(arrayformula(unique(mid(query(B2:B),6,1))), len(arrayformula(unique(mid(query(B2:B),6,1))))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),1,4))))), char(9999))))))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),1,4))))), char(9999))))),arrayformula(A2:A&" "&B2:B),1,0))),unique(arrayformula(transpose(split(join("", arrayformula(rept(filter(UNIQUE(A2:A), len(UNIQUE(A2:A)))&char(9999), counta(transpose(split(join("", arrayformula(rept(filter(arrayformula(unique(mid(query(B2:B),1,4))), len(arrayformula(unique(mid(query(B2:B),1,4)))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),6,1))))))), char(9999))) )))), char(9999))) &" "&transpose(split(rept(join(char(9999), filter(arrayformula((transpose(split(join("", arrayformula(rept(filter(arrayformula(unique(mid(query(B2:B),1,4))), len(arrayformula(unique(mid(query(B2:B),1,4)))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),6,1))))))), char(9999))) )&"."&(transpose(split(rept(join(char(9999), filter(arrayformula(unique(mid(query(B2:B),6,1))), len(arrayformula(unique(mid(query(B2:B),6,1))))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),1,4))))), char(9999))))), len(arrayformula((transpose(split(join("", arrayformula(rept(filter(arrayformula(unique(mid(query(B2:B),1,4))), len(arrayformula(unique(mid(query(B2:B),1,4)))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),6,1))))))), char(9999))) )&"."&(transpose(split(rept(join(char(9999), filter(arrayformula(unique(mid(query(B2:B),6,1))), len(arrayformula(unique(mid(query(B2:B),6,1))))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),1,4))))), char(9999))))))))&char(9999), counta(arrayformula(unique(mid(query(B2:B),1,4))))), char(9999))))),""))))