Home: go to the homepage U+2980 to U+29FF Miscellaneous Mathematical Symbols-B

# U+29E2Shuffle Product

U+29E2 was added in Unicode version 3.2 in 2002. It belongs to the block U+2980 to U+29FF Miscellaneous Mathematical Symbols-B in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script.

The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. The word that U+29E2 forms with similar adjacent characters prevents a line break inside it.

In mathematics, a shuffle algebra is a Hopf algebra with a basis corresponding to words on some set, whose product is given by the shuffle product XY of two words X, Y: the sum of all ways of interlacing them. The interlacing is given by the riffle shuffle permutation.

The shuffle algebra on a finite set is the graded dual of the universal enveloping algebra of the free Lie algebra on the set.

Over the rational numbers, the shuffle algebra is isomorphic to the polynomial algebra in the Lyndon words.

The shuffle product occurs in generic settings in non-commutative algebras; this is because it is able to preserve the relative order of factors being multiplied together - the riffle shuffle permutation. This can be held in contrast to the divided power structure, which becomes appropriate when factors are commutative.

## Representations

System Representation
10722
UTF-8 E2 A7 A2
UTF-16 29 E2
UTF-32 00 00 29 E2
URL-Quoted %E2%A7%A2
HTML hex reference &#x29E2;
Wrong windows-1252 Mojibake â§¢

## Complete Record

Property Value
Age (age) 3.2 (2002)
Unicode Name (na) SHUFFLE PRODUCT
Unicode 1 Name (na1)
Block (blk) Miscellaneous Symbols
General Category (gc) Math Symbol
Script (sc) Common
Bidirectional Category (bc) Other Neutral
Combining Class (ccc) Not Reordered
Decomposition Type (dt) none
Decomposition Mapping (dm) Shuffle Product
Lowercase (Lower)
Simple Lowercase Mapping (slc) Shuffle Product
Lowercase Mapping (lc) Shuffle Product
Uppercase (Upper)
Simple Uppercase Mapping (suc) Shuffle Product
Uppercase Mapping (uc) Shuffle Product
Simple Titlecase Mapping (stc) Shuffle Product
Titlecase Mapping (tc) Shuffle Product
Case Folding (cf) Shuffle Product
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Composition Exclusion (CE)
Case Ignorable (CI)
Changes When Casefolded (CWCF)
Changes When Casemapped (CWCM)
Changes When NFKC Casefolded (CWKCF)
Changes When Lowercased (CWL)
Changes When Titlecased (CWT)
Changes When Uppercased (CWU)
Cased (Cased)
Full Composition Exclusion (Comp_Ex)
Default Ignorable Code Point (DI)
Dash (Dash)
Deprecated (Dep)
Diacritic (Dia)
Emoji Modifier Base (EBase)
Emoji Component (EComp)
Emoji Modifier (EMod)
Emoji Presentation (EPres)
Emoji (Emoji)
Extender (Ext)
Extended Pictographic (ExtPict)
FC NFKC Closure (FC_NFKC) Shuffle Product
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hyphen (Hyphen)
ID Continue (IDC)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
IDSU (IDSU) 0
ID_Compat_Math_Continue (ID_Compat_Math_Continue) 0
ID_Compat_Math_Start (ID_Compat_Math_Start) 0
Ideographic (Ideo)
InCB (InCB) None
Indic Mantra Category (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
Jamo Short Name (JSN)
Join Control (Join_C)
Logical Order Exception (LOE)
Math (Math)
Noncharacter Code Point (NChar)
NFC Quick Check (NFC_QC) Yes
NFD Quick Check (NFD_QC) Yes
NFKC Casefold (NFKC_CF) Shuffle Product
NFKC Quick Check (NFKC_QC) Yes
NFKC_SCF (NFKC_SCF) Shuffle Product
NFKD Quick Check (NFKD_QC) Yes
Other Alphabetic (OAlpha)
Other Default Ignorable Code Point (ODI)
Other Grapheme Extend (OGr_Ext)
Other ID Continue (OIDC)
Other ID Start (OIDS)
Other Lowercase (OLower)
Other Math (OMath)
Other Uppercase (OUpper)
Prepended Concatenation Mark (PCM)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Regional Indicator (RI)
Sentence Break (SB) Other
Soft Dotted (SD)
Sentence Terminal (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) Other
White Space (WSpace)
XID Continue (XIDC)
XID Start (XIDS)
Expands On NFC (XO_NFC)
Expands On NFD (XO_NFD)
Expands On NFKC (XO_NFKC)
Expands On NFKD (XO_NFKD)
Bidi Paired Bracket (bpb) Shuffle Product
Bidi Paired Bracket Type (bpt) None
East Asian Width (ea) neutral
Hangul Syllable Type (hst) Not Applicable
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Joining Type (jt) Non Joining
Line Break (lb) Alphabetic
Numeric Type (nt) none
Numeric Value (nv) not a number
Simple Case Folding (scf) Shuffle Product
Script Extension (scx)
Vertical Orientation (vo) R