instructions_for_authors
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| We define the following additional macros. The purpose of those definitions is not only to make writing formulas easier but also to unify the notation for the wiki. So, authors are strongly encouraged to use the macros and to use them in the meaning specified in the table. If you suggest any changes in the list, please contact the administrators. | We define the following additional macros. The purpose of those definitions is not only to make writing formulas easier but also to unify the notation for the wiki. So, authors are strongly encouraged to use the macros and to use them in the meaning specified in the table. If you suggest any changes in the list, please contact the administrators. | ||
| - | ^ Symbol ^ Command ^ Meaning ^ | + | ^ Symbol ^ Command ^ Meaning ^ |
| - | |$\C$ | ''\C'' | Set of complex numbers | | + | |$\hatstar$ | ''\hatstar'' | Dual free product | |
| - | |$\GL$ | ''\GL'' | General linear group | | + | |$\tilstar$ | ''\tilstar'' | Glued free product | |
| - | |$\N$ | ''\N'' | Set of natural numbers (without zero) | | + | |$\tiltimes$ | ''\tiltimes'' | Glued tensor product | |
| - | |$\Part$ | ''\Part'' | Set of all partitions | | + | |$\C$ | ''\C'' | Set of complex numbers | |
| - | |$\R$ | ''\R'' | Set of real numbers | | + | |$\Cscr$ | ''\Cscr'' | Some category | |
| - | |$\spanlin$ | ''\spanlin'' | Linear span | | + | |$\FinHilb$ | ''\FinHilb'' | Category of finite-dimensional Hilbert spaces | |
| - | |$\Q$ | ''\Q'' | Set of rational numbers | | + | |$\FinVect$ | ''\FinVect'' | Category of finite-dimensional vector spaces | |
| - | |$\Z$ | ''\Z'' | Set of integers | | + | |$\FundRep$ | ''\FundRep'' | Category generated by the fundamental representation | |
| + | |$\GL$ | ''\GL'' | General linear group | | ||
| + | |$\Hilb$ | ''\Hilb'' | Category of Hilbert spaces | | ||
| + | |$\id$ | ''\id'' | Identity mapping | | ||
| + | |$\Irr$ | ''\Irr'' | Irreducible representations | | ||
| + | |$\Kscr$ | ''\Kscr'' | Some category | | ||
| + | |$\N$ | ''\N'' | Set of natural numbers (without zero) | | ||
| + | |$\Pol$ | ''\Pol'' | The Hopf algebra associated to CQG | | ||
| + | |$\Pscr$ | ''\Pscr'' | Set of all partitions | | ||
| + | |$\Part$ | ''\Part'' | Linear category of all partitions | | ||
| + | |$\R$ | ''\R'' | Set of real numbers | | ||
| + | |$\Rep$ | ''\Rep'' | Category of representations | | ||
| + | |$\spanlin$ | ''\spanlin'' | Linear span | | ||
| + | |$\T$ | ''\T'' | Complex unit circle | | ||
| + | |$\Q$ | ''\Q'' | Set of rational numbers | | ||
| + | |$\Vect$ | ''\Vect'' | Category of vector spaces | | ||
| + | |$\Z$ | ''\Z'' | Set of integers | | ||
| ==== Partitions ==== | ==== Partitions ==== | ||
| - | For typesetting partitions, we use the macro package ''partmac'' from [[https://www.math.uni-sb.de/ag/speicher/gromadaE.html|Daniel Gromada]]. Here are the instructions | + | For typesetting partitions, we use the macro package ''partmac'' from [[https://www.math.uni-sb.de/ag/speicher/gromadaE.html|Daniel Gromada]]. For more details, see [[Typesetting partitions]]. |
| - | + | ||
| - | === Predefined partitions === | + | |
| - | + | ||
| - | There are macros of the form ''\Lxxxx'' for partitions on lower line, ''\Uxxxx'' for partitions on upper line and ''\Pxxxx'' for partitions with the same ammount of upper and lower points. Here ''xxxx'' is the lexicographically smallest word representation of the partiiton. That is, we have the following macros for partitions with points on the lower line. | + | |
| - | + | ||
| - | |''\La'' | $\La$ | ''\Laaaa'' | $\Laaaa$ | ''\Laabc'' | $\Laabc$ | | + | |
| - | |''\Laa'' | $\Laa$ | ''\Laaab'' | $\Laaab$ | ''\Labac'' | $\Labac$ | | + | |
| - | |''\Lab'' | $\Lab$ | ''\Laaba'' | $\Laaba$ | ''\Labca'' | $\Labca$ | | + | |
| - | |''\Laaa'' | $\Laaa$ | ''\Labaa'' | $\Labaa$ | ''\Labbc'' | $\Labbc$ | | + | |
| - | |''\Laab'' | $\Laab$ | ''\Labbb'' | $\Labbb$ | ''\Labcb'' | $\Labcb$ | | + | |
| - | |''\Laba'' | $\Laba$ | ''\Laabb'' | $\Laabb$ | ''\Labcc'' | $\Labcc$ | | + | |
| - | |''\Labb'' | $\Labb$ | ''\Labba'' | $\Labba$ | ''\Labcd'' | $\Labcd$ | | + | |
| - | |''\Labc'' | $\Labc$ | ''\Labab'' | $\Labab$ | | + | |
| - | + | ||
| - | Then we have the following macros for partitions with points on the upper line. | + | |
| - | + | ||
| - | |''\Ua'' | $\Ua$ | ''\Uaaaa'' | $\Uaaaa$ | ''\Uaabc'' | $\Uaabc$ | | + | |
| - | |''\Uaa'' | $\Uaa$ | ''\Uaaab'' | $\Uaaab$ | ''\Uabac'' | $\Uabac$ | | + | |
| - | |''\Uab'' | $\Uab$ | ''\Uaaba'' | $\Uaaba$ | ''\Uabca'' | $\Uabca$ | | + | |
| - | |''\Uaaa'' | $\Uaaa$ | ''\Uabaa'' | $\Uabaa$ | ''\Uabbc'' | $\Uabbc$ | | + | |
| - | |''\Uaab'' | $\Uaab$ | ''\Uabbb'' | $\Uabbb$ | ''\Uabcb'' | $\Uabcb$ | | + | |
| - | |''\Uaba'' | $\Uaba$ | ''\Uaabb'' | $\Uaabb$ | ''\Uabcc'' | $\Uabcc$ | | + | |
| - | |''\Uabb'' | $\Uabb$ | ''\Uabba'' | $\Uabba$ | ''\Uabcd'' | $\Uabcd$ | | + | |
| - | |''\Uabc'' | $\Uabc$ | ''\Uabab'' | $\Uabab$ | | + | |
| - | + | ||
| - | Finally partitions with equal number of points on lower and upper line. | + | |
| - | + | ||
| - | |''\Paa'' | $\Paa$ | ''\Pabab'' | $\Pabab$ | ''\Pabcabc'' | $\Pabcabc$ | | + | |
| - | |''\Pab'' | $\Pab$ | ''\Paabc'' | $\Paabc$ | ''\Pabcabd'' | $\Pabcabd$ | | + | |
| - | |''\Paaaa'' | $\Paaaa$ | ''\Pabac'' | $\Pabac$ | ''\Pabcadc'' | $\Pabcadc$ | | + | |
| - | |''\Paaab'' | $\Paaab$ | ''\Pabca'' | $\Pabca$ | ''\Pabcdbc'' | $\Pabcdbc$ | | + | |
| - | |''\Paaba'' | $\Paaba$ | ''\Pabbc'' | $\Pabbc$ | ''\Pabcade'' | $\Pabcade$ | | + | |
| - | |''\Pabaa'' | $\Pabaa$ | ''\Pabcb'' | $\Pabcb$ | ''\Pabcdbe'' | $\Pabcdbe$ | | + | |
| - | |''\Pabbb'' | $\Pabbb$ | ''\Pabcc'' | $\Pabcc$ | ''\Pabcdec'' | $\Pabcdec$ | | + | |
| - | |''\Paabb'' | $\Paabb$ | ''\Pabcd'' | $\Pabcd$ | ''\Pabcdef'' | $\Pabcdef$ | | + | |
| - | |''\Pabba'' | $\Pabba$ | + | |
| - | + | ||
| - | In addition, we define the following synonyms. | + | |
| - | + | ||
| - | |''\singleton'' | $\singleton$ | ''\idpart'' | $\idpart$ | ''\fourpart'' | $\fourpart$ | | + | |
| - | |''\upsingleton'' | $\upsingleton$ | ''\disconnecterpart'' | $\disconnecterpart$ | ''\crosspart'' | $\crosspart$ | | + | |
| - | |''\pairpart'' | $\pairpart$ | ''\positionerpart'' | $\positionerpart$ | ''\halflibpart'' | $\halflibpart$ | | + | |
| - | |''\uppairpart'' | $\uppairpart$ | ''\connecterpart'' | $\connecterpart$ | | + | |
instructions_for_authors.1551427988.txt.gz · Last modified: 2021/11/23 11:56 (external edit)
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