منابع مشابه
Compositions inside a rectangle and unimodality
Let c(n) be the number of compositions (ordered partitions) of the integer n whose Ferrers diagram fits inside a k× l rectangle. The purpose of this note is to give a simple, algebraic proof of a conjecture of Vatter that the sequence c(0), c(1), . . . , c(kl) is unimodal. The problem of giving a combinatorial proof of this fact is discussed, but is still open.
متن کاملCounting Partitions of Graphs
Recently, there has been much interest in studying certain graph partitions that generalize graph colourings and homomorphisms. They are described by a pattern, usually viewed as a symmetric {0, 1, ∗}matrix M . Existing results focus on recognition algorithms and characterization theorems for graphs that admit such M -partitions, or M partitions in which vertices of the input graph G have lists...
متن کاملAsymptotic normality of integer compositions inside a rectangle
Among all restricted integer compositions with at most m parts, each of which has size at most l, choose one uniformly at random. Which integer does this composition represent? In the current note, we show that underlying distribution is, for large m and l, approximately normal with mean value ml 2 .
متن کاملAn oscillating C2(2-) unit inside a copper rectangle.
[Cu4(mu-dppm)4(mu4-eta1,eta2-C[triple bond]C-)]2+ has been shown by 31P and 1H NMR studies to undergo two fluxional processes in solution, the oscillation of the C[triple bond]C2- unit inside the copper rectangle and the flipping of the diphosphines, and this has been supported by DFT(B3LYP) calculations.
متن کاملCounting Partitions of a Fixed Genus
We show that, for any fixed genus g, the ordinary generating function for the genus g partitions of an n-element set into k blocks is algebraic. The proof involves showing that each such partition may be reduced in a unique way to a primitive partition and that the number of primitive partitions of a given genus is finite. We illustrate our method by finding the generating function for genus 2 ...
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: SIAM Journal on Discrete Mathematics
سال: 2020
ISSN: 0895-4801,1095-7146
DOI: 10.1137/20m1315828