A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Recurrences for 2-colored and 3-colored F-partitions

1996
*
Discrete Mathematics
*

The goal of this paper is to prove new

doi:10.1016/0012-365x(95)00059-6
fatcat:rz2srbabybcpba7kszcjhh3gsi
*recurrences*involving*2*-*colored**and**3*-*colored*generalized Frobenius*partitions*of n similar to the classical*recurrence**for*the*partition*function p(n ). ... The goal of this paper is to prove five new*recurrences*similar to (1.1) involving*2*-*colored**and**3*-*colored*generalized Frobenius*partitions*, or*F*-*partitions*. ... Here we define C~)m(n) as the number of*F*-*partitions*of n using m*colors*[*2*] . Then C~)m(n) is the number of*F*-*partitions*of n using m*colors*whose order under cyclic permutation of the*colors*is m. ...##
###
Partition Recurrences
[article]

2018
*
arXiv
*
pre-print

We present some Euler-type

arXiv:1811.09206v1
fatcat:kj5tbx4qdzevnahmpnnasda3h4
*recurrences**for*the*partition*function p(n). ... Acknowledgments We thank Dennis Eichhorn*and*James Sellers*for*pointing us to several relevant references in the literature,*and*the anonymous referee who read our manuscript carefully*and*pointed out ... We thank Bruce Landman*for*organizing the INTEGERS 2016 conference, which facilitated the first*and*third authors becoming aware of the second author's earlier unpublished work on this topic. ...##
###
On colored set partitions of type B n

2014
*
Open Mathematics
*

Considering the generating function of

doi:10.2478/s11533-014-0419-9
fatcat:dinavoz7tfeadj2ay6mvrfzeu4
*colored*B n-*partitions*, we get the exact formulas*for*the expectation*and*variance of the number of non-zero-blocks in a random*colored*B n-*partition*. ... We find an asymptotic expression of the total number of*colored*B n-*partitions*up to an error of O(n −1/2log7/*2*n],*and*prove that the centralized*and*normalized number of non-zero-blocks is asymptotic ... Acknowledgements The author is grateful to the anonymous referee*for*the suggestion of generalizing the original -version problem to the present ( )-version problem,*and**for*bringing Dowling's paper to ...##
###
Counting Latin rectangles

1987
*
Bulletin of the American Mathematical Society
*

Explicit formulas

doi:10.1090/s0273-0979-1987-15465-6
fatcat:2m6fsvfo2vhnxbsgmopk7n4jte
*for*fc =*3*are fairly well known [1-*3*, 4, pp. 284-286*and*506-507, 5, 6, 9-11, 12, pp. 204-210]. ... We use properties of the Möbius functions of*partition*lattices, as did Bogart*and*Longyear [*2*], Pranesachar et al. [1, 9] ,*and*Nechvatal [8], but in a somewhat different way. ... Explicit formulas*for*fc =*3*are fairly well known [1] [*2*] [*3*] 4 , pp. 284-286*and*506-507, 5, 6, 9-11, 12, pp. 204-210]. Formulas*for*fc = 4 were found by Pranesachar et al. ...##
###
Stanley–Elder–Fine theorems for colored partitions
[article]

2021
*
arXiv
*
pre-print

More specifically, we give analogous results

arXiv:2102.03486v2
fatcat:b5va67p5kjcqjn3cil5z7mojle
*for*b-*colored**partitions*, where each part occurs in b*colors*;*for*b-*colored**partitions*with odd parts (or distinct parts);*for**partitions*where the part k comes ... in k*colors*;*and*, overpartitions. ...*For*example, the*partition*4+*3*+*3*+*2*+1+1+1+1 has frequencies:*f*1 = 4,*f**2*= 1,*f**3*=*2*,*f*4 = 1. One of the quantities in the Stanley-Elder-Fine theorem is*for*k = 1,*2*, . . . , n. ...##
###
Exact and Fixed Parameter Tractable Algorithms for Max-Conflict-Free Coloring in Hypergraphs

2018
*
SIAM Journal on Discrete Mathematics
*

In this paper, we initiate a study of a natural maximization version of this problem, namely, Max-CFC:

doi:10.1137/16m1107462
fatcat:g5ec3lysbfhc5igpndcfdx7kvy
*For*a given hypergraph H*and*a fixed r ≥*2*,*color*the vertices of U using r*colors*so that the number ...*For*a hypergraph H = (U,*F*), a conflict-free*coloring*of H refers to a vertex*coloring*where every hyperedge has a vertex with a unique*color*, distinct from all other vertices in the hyperedge. ... Lemmas 16, 17 ,*and*the safeness of the reduction rules*2*,*3*, 4, 5 together result in the following algorithm*for**Partitioned*p-CFC. Lemma 18. ...##
###
Crossings and nestings in colored set partitions
[article]

2013
*
arXiv
*
pre-print

*and*

*2*-Motzkin paths. ... Chen, Deng, Du, Stanley,

*and*Yan introduced the notion of k-crossings

*and*k-nestings

*for*set

*partitions*,

*and*proved that the sizes of the largest k-crossings

*and*k-nestings in the

*partitions*of an n-set ... Acknowledgements I am grateful to Cyril Banderier, Joel Brewster Lewis, Alejandro Morales, Alexander Postnikov, Steven V Sam,

*and*Richard P. Stanley

*for*helpful discussions

*and*suggestions. ...

##
###
Detecting Recurrence Domains of Dynamical Systems by Symbolic Dynamics

2013
*
Physical Review Letters
*

We propose an algorithm

doi:10.1103/physrevlett.110.154101
pmid:25167271
fatcat:vaq4tyav55anznt3bh2wxw7qja
*for*the detection of*recurrence*domains of complex dynamical systems from time series. ... Our approach exploits the characteristic checkerboard texture of*recurrence*domains exhibited in*recurrence*plots (RP). ... (e) Phase space*partition*into*recurrence*domains*for*optimal encoding ε * = 1.9. (*f*) Symbolic*recurrence*plot [Eq. (*2*)] of optimal encoding. ...##
###
A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

1994
*
Electronic Journal of Combinatorics
*

*For*$k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$

*and*on the k-

*color*Ramsey numbers of $K_3$. ...

*For*Ramsey numbers we know R

*2*(

*3*) = 6

*and*R

*3*(

*3*) = 17; the current bounds on R 4 (

*3*) are 51

*and*65 [5] . ... Then define:

*f*1 (P ) = max{t|P t is sum-free}

*f*

*2*(P ) = k i=1 s,t∈Si g n (s, t)

*and*finally

*f*(P ) = c 1

*f*1 (P ) + c

*2*

*f*

*2*(P ). ...

##
###
n-Color partitions with weighted differences equal to minus two

1997
*
International Journal of Mathematics and Mathematical Sciences
*

It is shown how these

doi:10.1155/s016117129700104x
fatcat:sngiow7eczdenhhc3y4w62ngtm
*partitions*arise in the study of conjugate*and*self-conjugaten-*color**partitions*. A combinatorial identity*for*self-conjugaten-*color**partitions*is also obtained. ... In this paper we study thosen-*color**partitions*of Agarwal*and*Andrews, 1987, in which each pair of parts has weighted difference equal to−2Results obtained in this paper*for*these*partitions*include several ... the conjugate of H*and*will be denoted by lI*For*example, if we consider YI 52 +*3*, an n-*color**partition*of 8, then l'I 55-*2*+1 + 33-+ 54 + 33 DEFINITION*2*. ...##
###
A Computer Proof of a Polynomial Identity Implying a Partition Theorem of Göllnitz

2002
*
Advances in Applied Mathematics
*

In addition, we provide computer proofs

doi:10.1006/aama.2001.0764
fatcat:454eqrs3mzhnrcwus6rt6qubq4
*for*new finite analogs of Jacobi*and*Euler formulas. ... In this paper we give a computer proof of a new polynomial identity, which extends a recent result of Alladi*and*the first author. ... Andrews,*and*Doron Zeilberger*for*their interest*and*comments on the manuscript. ...##
###
Stirling Numbers of Forests and Cycles

2013
*
Electronic Journal of Combinatorics
*

Along the way we give

doi:10.37236/3170
fatcat:dumts6dakneoxjrsvj4jiswkfm
*recurrences**for*calculating the generating functions of the sequences $(S(*F*^c_n,k))_{k \geq 0}$, show that these functions have all real zeroes,*and*exhibit three different interlacing ...*For*a graph $G$*and*a positive integer $k$, the graphical Stirling number $S(G,k)$ is the number of*partitions*of the vertex set of $G$ into $k$ non-empty independent sets. ... Indeed, given a palette of x*colors*,*for*each k there are S(G, k) ways to*partition*the vertex set into k non-empty*color*classes,*and*x (k) ways to assign*colors*the classes. ...##
###
Stirling numbers of forests and cycles
[article]

2012
*
arXiv
*
pre-print

Along the way we give

arXiv:1206.3591v1
fatcat:xyyrufeojbab7frt2glb2g36xq
*recurrences**for*calculating the generating functions of the sequences (S(*F*^c_n,k))_k ≥ 0, show that these functions have all real zeroes,*and*exhibit three different interlacing patterns ...*For*a graph G*and*a positive integer k, the graphical Stirling number S(G,k) is the number of*partitions*of the vertex set of G into k non-empty independent sets. ... Indeed, given a palette of x*colors*,*for*each k there are S(G, k) ways to*partition*the vertex set into k non-empty*color*classes,*and*x (k) ways to assign*colors*the classes. ...##
###
Chunking as a rational strategy for lossy data compression in visual working memory

2018
*
Psychological review
*

We show that such chunking can: 1) facilitate performance 7 improvements

doi:10.1037/rev0000101
pmid:29952621
pmcid:PMC6026019
fatcat:ztijqj33wzbyrkttihr3pxwgdi
*for*abstract capacity-limited systems,*2*) be optimized through 8 reinforcement,*3*) be implemented by center-surround dynamics,*and*... The nature of capacity limits*for*visual working memory has been the*3*subject of an intense debate that has relied on models that assume items are 4 encoded independently. ... Capacity limitations are modeled by a fixed limit on the*2*length of the resulting "sentence" comprised of*color**and*orientation words separated by word*3*termination symbols (*2*/*3**for**color*/orientation ...##
###
Probabilistic analysis of algorithms for the Dutch national flag problem

2005
*
Theoretical Computer Science
*

A detailed probabilistic analysis is given of algorithms

doi:10.1016/j.tcs.2005.03.047
fatcat:53cyivliqjetxjnpu4d2orsi2i
*for*the Dutch national flag problem. We derive central*and*local limit theorems*for*the cost, as well as probabilities of large deviations. ... Then*F*n (y) satisfies the*recurrence**F*n (y) = y n−*2*j =0 n − j − 1*2*n−j*F*j (y) + n + 1*2*n (n*2*), (1) with*F*0 (y) =*F*1 (y) = 1. Proof. ... Then H n (y) satisfies the*recurrence*H n (y) = 1*3*n + 1 + y*3*H n−1 (y) + (y*2*+ y) n−*2*j =0 H j (y)*3*n−j (n*2*), (*3*) with H 0 (y) = 1*and*H 1 (y) = (*2*+ y)/*3*. Proof. ...
« Previous

*Showing results 1 — 15 out of 23,403 results*