Monotone Triangles and 312 Pattern Avoidance
نویسندگان
چکیده
منابع مشابه
Combinatorial reciprocity for Monotone Triangles
The number of Monotone Triangles with bottom row k1 < k2 < · · · < kn is given by a polynomial α(n; k1, . . . , kn) in n variables. The evaluation of this polynomial at weakly decreasing sequences k1 ≥ k2 ≥ · · · ≥ kn turns out to be interpretable as signed enumeration of new combinatorial objects called Decreasing Monotone Triangles. There exist surprising connections between the two classes o...
متن کاملTrivial Meet and Join within the Lattice of Monotone Triangles
The lattice of monotone triangles (Mn,≤) ordered by entry-wise comparisons is studied. Let τmin denote the unique minimal element in this lattice, and τmax the unique maximum. The number of r-tuples of monotone triangles (τ1, . . . , τr) with minimal infimum τmin (maximal supremum τmax, resp.) is shown to asymptotically approach r|Mn| as n → ∞. Thus, with high probability this event implies tha...
متن کاملPattern Avoidance
Consider a sequence of letters or numbers. Does a pattern exist that is avoided by the sequence? This topic is a very popular area of research in mathematics for its promising utility in computer science and other branches of mathematics, the elegant proofs and solutions, and the many open problems that still remain. Section 1 of this paper provides definitions, notations, and some properties o...
متن کاملGeneralized monotone triangles – an extended combinatorial reciprocity theorem
In a recent work, the combinatorial interpretation of the polynomial α(n; k1, k2, . . . , kn) counting the number of Monotone Triangles with bottom row k1 < k2 < · · · < kn was extended to weakly decreasing sequences k1 ≥ k2 ≥ · · · ≥ kn. In this case the evaluation of the polynomial is equal to a signed enumeration of objects called Decreasing Monotone Triangles. In this paper we define Genera...
متن کاملInfinite Sequences and Pattern Avoidance
The study of combinatorics on words dates back at least to the beginning of the 20 century and the work of Axel Thue. Thue was the first to give an example of an infinite word over a three letter alphabet that contains no squares (identical adjacent blocks) xx. This result was eventually used to solve some longstanding open problems in algebra and has remarkable connections to other areas of ma...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/2022