Leptary Flags (collection)
Equigender/Neugender Arity (neutrois/equitrois/equitive arity/neuarity/n-ary neutrality/equity/equitivity): equarity/equinarity/parity (equiry/equinary or aquary/pary/neutrary).
Nongender Arity (non-arial/non-ary): anarity (an-ary/niladic), nonunarity (nonunary/nonmonary/nonsingulary), nonbinarity/nonbinaryness and nonternarity/nontrinarity (nontrinary/nonternary).
Agender Arity (niladicity): nullarity (nullary), abinarity (abinary) and aternarity/atrinarity (aternary/atrinary).
Leptarity means gender arity, which includes number of pre-established/existing (implied or subsequent) gender items/bases/entry within your culture. Most people know the Western gender binarity, in which male & female are embedded into binary category system/radix.
But what could be considered gender unary/monary/singulary or trinary? Unarity (monarity/singularity) would only include primarity while trinarity would be binarity but also including tertiarity. The primary identity would be any binarie, depending on your culture, binaries could not even exist, so everyone would be expected to be/have only one specific gender. The tertiary identity would be a third-identity (or third-gender/aliagender), neutrois/neuter, genderless/neither, androgyne/both or nonbinary/abinary as monogender itself.
The gender ternarity isn’t so clear, it could also encompass another quadnarity/quadrinarity (quadrinary), that’s why who coined it worded first qua/ternary (I think there’s a flag for a(qua)ternary/non(qua)ternary but I didn’t find).
There are also cultures with five (quinary) or six (senary/hexary) genders (quinarity/quintarity or hexarity/senarity), so some other identities couldn’t be classified intrinsically as second/ary (secondarity), fourth (quadnary), fifth (quintary) or sixth one(s).
Nullary would mean not being limited/linked to your own cultural arities or any arity at all/in general. Similar to equary, but equirity means all gender entries are equal. Ask me if in doubt.