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  "body": "\n## Definition\n\nA Dyck word is a finite word $w$ over the two-letter alphabet $\\{U, D\\}$ with these two properties.\nThe word $w$ has as many letters $U$ as letters $D$.\nEach prefix of $w$ has at least as many letters $U$ as letters $D$.\n\nThe semilength of a Dyck word is its number of letters $U$, which is half its length.\n\n## Remarks\n\nOther common alphabets are $\\{(, )\\}$ and $\\{[, ]\\}$. Then the Dyck words are the balanced strings of brackets.\nThe Dyck words of semilength $2$ are $UUDD$ and $UDUD$.\nRead $U$ as a step $(1, 1)$ and $D$ as a step $(1, -1)$. A Dyck word is then a [[lattice path|040WY0TT2G]] from $(0, 0)$ to $(2n, 0)$ that never goes below the horizontal axis.\nThe Dyck words of semilength $n$ are [[counted by the Catalan number|017SRZ7NE9]] $C_n$.\n\n## Explanations\n\n### L1 human\n\nA Dyck word is a correct sequence of opening and closing brackets.\nThe sequence $(()())$ is a Dyck word, but $())($ is not, because after three symbols there are more closing than opening brackets.\n",
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        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
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