Quote: Starting with basics, a gene is a piece of DNA occupying a specific place on a specific chromosome. The exact makeup of the DNA determines its allele. To put it another way, alleles are different variations, or mutations of a gene. In most cases chromosomes occur in matched pairs; however for the sex chromosomes, the pair are not matched. One is longer than the other, and the genes that occur on this longer chromosome are referred to as being sex-linked. In birds, these sex chromosomes are Z (the longer one) and W. Males are ZZ and females are ZW. Thus females have only one of each sex-linked gene while males have two.
The symbol for recessive white is c, and it is autosomal (not sex-linked). A lower case symbol indicates a recessive allele; an upper case one indicates a dominant allele. For the sake of simplicity, let's ignore the very uncommon red-eye and albino recessive white alleles and deal only with normal recessive white and its opposite, not-recessive-white, C+. Being recessive, c only expresses when a more dominant allele is not present, therefore a bird must be c/c for recessive white to show in the appearance of the bird. A bird that is C+/c carries (or is split to) recessive white, and can pass the gene to its offspring, but dos not express recessive white itself. Only breeding history can tell you whether a bird is split to recessive white. On a cellular level, the recessive white gene prevents the creation of all pigment for feathers. For a bird to be recessive white, it does not matter what other colour or pattern genes it carries, all it needs is c/c.
Partridge requires that a bird be brown (e^b) based, have gold (s+) ground and the pattern gene (Pg). There should also be no genes that dilute either pigment, and enhancing gold pigment with mahogany is desired.
Splash requires two copies of blue: Bl/Bl. Black requires two copies of not-blue: bl+/bl+. Blue requires one copy of the blue gene and one copy of not-blue: B/bl+. Technically, blue should also carry the genes for lacing: Pg Ml and Co, but lacing does not show well on silkie feathers, and I doubt that many blue silkies are genetically laced. These three varieties can be either silver or gold. Being a sex-linked gene, males can also carry a copy of each (S/s+), while females are one or the other (S/- or s+/-).
Chick down indicates some genes the birds carry. White or silvery chick down indicates a bird with silver; yellow down indicates a bird with gold. Some lines tend to be more of one or the other.