Combinatorial enumeration of 2×2 ribbon patterns
نویسندگان
چکیده
An algorithm for creating repeating patterns from a single decorated square gives rise to an obvious combinatorial question: How many different patterns can be created, following the rules? Answers vary according to the definition of equivalence of patterns, and computer sorting programs can provide numerical answers. But algebraic techniques give insight into the answers and provide general formulas for similar problems. Group actions on signatures assigned to patterns can also determine which patterns have symmetry. c © 2006 Elsevier Ltd. All rights reserved.
منابع مشابه
Signed enumeration of ribbon tableaux: an approach through growth diagrams
We give an extension of the famous Schensted correspondence to the case of ribbon tableaux, where ribbons are allowed to be of different sizes. This is done by extending Fomin’s growth diagram approach of the classical correspondence, in particular by allowing signs in the enumeration. As an application, we give in particular a combinatorial proof, based on the Murnaghan–Nakayama rule, for the ...
متن کاملHalf-Century Journey from Synthetic Organic Chemistry to Mathematical Stereochemistry through Chemoinformatics
My half-century journey started from synthetic organic chemistry. During the first stage of my journey, my interest in stereochemistry was initiated through the investigation on the participation of steric effects in reactive intermediates, cylophanes, strained heterocycles, and organic compounds for photography. In chemoinformatics as the next stage of the journey, I proposed the concept of im...
متن کاملType-Itemized Enumeration of RS-Stereoisomers of Octahedral Complexes
Stereoisograms of octahedral complexes are classified into five types (type I--typeV) under the action of the corresponding RS-stereoisomeric group. Their enumeration is accomplished in a type-itemized fashion, where Fujita's proligand method developed originally for combinatorial enumeration under point groups (S. Fujita, Theor. Chem. Acc., 113, 73--79 (2005)) is extended to meet the requireme...
متن کاملar X iv : 1 51 0 . 05 43 4 v 2 [ m at h . C O ] 2 9 O ct 2 01 5 Patterns in Inversion Sequences
Permutations that avoid given patterns have been studied in great depth for their connections to other fields of mathematics, computer science, and biology. From a combinatorial perspective, permutation patterns have served as a unifying interpretation that relates a vast array of combinatorial structures. In this paper, we introduce the notion of patterns in inversion sequences. A sequence (e1...
متن کامل2 00 4 COMBINATORIAL CLASSES ON M g , n ARE
The combinatorial description via ribbon graphs of the moduli space of Riemann surfaces makes it possible to define combinatorial cycles in a natural way. Witten and Kontsevich first conjectured that these classes are polynomials in the tautological classes. We answer affirmatively to this conjecture and find recursively all the polynomials.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Eur. J. Comb.
دوره 28 شماره
صفحات -
تاریخ انتشار 2007