Postgres 13

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Help with an interesting Postgres question: Why isn't an Index Only Scan used on a partition accessed via the parent table?.

CREATE TABLE Element
(
  Element  CHAR(1)  NOT NULL COLLATE "en_US" /* Chosen since a < A < B < C.  Case support varies by Postgres version, check constraint handles this */
 ,CONSTRAINT PK_Element PRIMARY KEY (Element)
 ,CONSTRAINT CK_Element_Is_Uppercase CHECK (Element = UPPER(Element))
)

CREATE TABLE

INSERT INTO Element VALUES ('A'),('B'),('C'),('D')

INSERT 0 4

WITH RECURSIVE Tuple AS
(
  SELECT
    CAST(Element AS Text) AS Tuple
   ,1 AS TupleLength
  FROM
    Element
  
    UNION ALL
    
  SELECT
    T.Tuple || E.Element
   ,TupleLength + 1
  FROM
    Tuple T
  INNER JOIN
    Element E
      ON E.Element >= RIGHT(T.Tuple,1)
  WHERE
    TupleLength < (SELECT COUNT(*) FROM Element)
)
SELECT
  Tuple
FROM
  Tuple
ORDER BY
  TupleLength
 ,Tuple

tuple

A

B

C

D

AA

AB

AC

AD

BB

BC

BD

CC

CD

DD

AAA

AAB

AAC

AAD

ABB

ABC

ABD

ACC

ACD

ADD

BBB

BBC

BBD

BCC

BCD

BDD

CCC

CCD

CDD

DDD

AAAA

AAAB

AAAC

AAAD

AABB

AABC

AABD

AACC

AACD

AADD

ABBB

ABBC

ABBD

ABCC

ABCD

ABDD

ACCC

ACCD

ACDD

ADDD

BBBB

BBBC

BBBD

BBCC

BBCD

BBDD

BCCC

BCCD

BCDD

BDDD

CCCC

CCCD

CCDD

CDDD

DDDD

SELECT 69