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Gröbner bases of balanced polyominoes
Author(s) -
Herzog Jürgen,
Qureshi Ayesha Asloob,
Shikama Akihiro
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400153
Subject(s) - polyomino , mathematics , combinatorics , monomial , square free integer , ideal (ethics) , regular polygon , simple (philosophy) , prime (order theory) , tree (set theory) , order (exchange) , discrete mathematics , geometry , law , philosophy , epistemology , finance , political science , economics
We introduce balanced polyominoes and show that their ideal of inner minors is a prime ideal and has a squarefree Gröbner basis with respect to any monomial order, and we show that any row or column convex and any tree‐like polyomino is simple and balanced.