Concept

Lapping — where it appears

The path a warp-knitting guide takes across the needles between courses, written as a number sequence. Whether the lapping joins its wales is an arithmetic condition on that sequence rather than a matter of degree.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as tricot, warp knitting — the same set of essays touches all of them, so they are one junction rather than several.

The tricot lapping. A warp-knit lapping drawn from the guide bar's movement. Each thread is coloured by the group of wales it belongs to, so a lapping that leaves the wales independent shows as several colours. This one joins them into 1 group.

Warp knitting, which is a different thing entirely

Every wale has its own thread, and if the thread never leaves its wale the fabric is a set of independent cords. Whether a lapping makes cloth is decided by a coprimality condition — the satin theorem, in a knit.

knits · Warp knit

What a second guide bar buys. Independent fabrics left by each lapping across 12 wales, counted by walking the wale graph and checked against the greatest common divisor of the shogs with the width. A bar that leaves more than one is not making cloth; a second bar can put right what the first could not.

What a second guide bar is for

One warp-knit bar leaves the wales in as many independent fabrics as its shog shares factors with the width. Two bars leave the greatest common divisor of both — so a pair of shogs that each fail alone can succeed together, and a pair that share a factor cannot.

knits · Warp knit

Named alongside it

The objects these essays reach for when they reach for this one.

Tricot Wale Warp knitting Cloth integrity Connectivity Greatest common divisor

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