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Rangers fan forced to visit Celtic store after Ibrox club shop runs out of letters for back of his strip

Andrew Grant had to make an embarrassing appearance 'behind enemy lines' to get Mr and Mrs Gers strips as a wedding present for his pal.
Rangers fan forced to visit Celtic store after Ibrox club shop runs out of letters for back of his strip
[07-17] Rangers 3 Celtic 2...Amazing Penny Arcade & Blue Sea Of Ibrox - High Q... via @YouTube #rangers #ibrox #scotland
[07-17] @BBCSportsound @RangersFC Stripped of titles. Club forced into liquidation and Ibrox flattened. Minter club minter fans. #Scotland's #Shame
[07-17] Former Rangers man: Pedro Caixinha forced me to leave Ibrox- #RangersFC #RFC #Gers
[07-17] #Glasgow #Rangers #9IAR Naismith is definitely not coming back to Ibrox, 100%
[08-17] Visit home of #Glasgow #Rangers, #Ibrox Stadium via @YouTube
[08-17] Hibs win at Ibrox and Lennon let's his Celtic connections show... #celticfc #Rangers #Hibs
[07-17] BIGGEST CLUB: RT for Rangers, favourite for Celtic. #SPFL #Glasgow #Scotland
[07-17] #Glasgow #Rangers #9IAR Do we really believe that the board who brought Warbs & Ped to the club are the ppl to take us back to the top?
[08-17] Get kitted out like the champions - shop in-store and online #Celtic #Celticfc #Bhoys #FNH
[08-17] Patrick Roberts wearing Celtic strip in Manchester City website profile #Celtic #Celticfc #Bhoys #FNH
[08-17] #Celtic to visit #Dundee in League Cup, #Rangers away to Partick Thistle
[07-17] Back to when I painted a mates garden in Celtic stripes when he is a die hard Rangers fan #RangersFC #celticfc #oldfirm #…
[07-17] Shop the #SoloSale today! Visit to see what's in store and catch up on our latest blogs…
[07-17] At 6: Dave King hits back at #Celtic and defends #Rangers use of EBTs & #Manchesterattack vicitm moved to #Glasgow
[08-17] Celtic face Patrick Roberts sweat as clock runs down to deadline for Ch #Celtic #Celticfc #Bhoys #FNH
[07-17] #Birmingham shooting: Gun fired outside Broad Street strip club via @po_st #LapDancing
[07-17] #Birmingham strip club facing criminal probe after 'customers were offered sex, drugged and ripped off'…
[07-17] Trading standards and police report alleges #Birmingham strip club Legs 11 conned customers out of £93,000 over the…
Kenny Miller celebrates opening the scoring vs Celtic at Ibrox. Scottish Premiership. 31st December 2016.
What is the number of binary strings of length N with exactly R runs of ones, with C total ones?
I'm concerned with the total number of ones, and the total number of runs, but not with the size of any of the runs. For example, $N=8$, $R=3$, $C=5$ includes 11101010, 01101011 among the 24 total possible strings. I can compute these for small $N$ easily enough, but I am specifically interested in the distribution for $N=65536$. As this will result in very large integers, the log probability distribution is equally useful. I found [1] and [2], which includes this: Let $N_{n;g_k,s_k}$ denote the number of binary strings which contain for given $g_k$ and $s_k$, $g_k=0,1,…,⌊\frac{s_k}{k}⌋$, $s_k=0,k,k+1,…,n$, exactly $g_k$ runs of 1’s of length at least $k$ with total number of 1’s (with sum of lengths of runs of 1’s) exactly equal to $s_k$ in all possible binary strings of length $n$. An expression for this is given in eq. (24): $N_{n;g_k,s_k} = \sum_{y=0}^{n-s_k} {y+1 \choose g_k } {s_k-(k-1)g_k-1 \choose g_k-1} \sum_{j=0}^{⌊\frac{n-y-s_k}{k}⌋} (-1)^j {y+1+g_k \choose j} {n-s_k-kj-g_k \choose n-s_k-kj-y} $ for $g_k \in \{1, ..., ⌊\frac{s_k}{k}⌋\}$, $s_k \in \{k, k+1, ..., n\}$. I think this is exactly what I'm looking for, with $k = 1$, $s_k = C$ and $g_k = R$. However, when I implemented this I did not get the expected results (Python shown below, edge cases omitted), based on comparing to counting all strings for N=8. I am working backwards to try to understand where I might have gone wrong, but not having much luck yet. I wonder if I am misunderstanding the result. def F(x, y, n): # x = C or s_k (cardinality) # y = R or g_k (runCount) # n = N (total bits) a1 = 0 for z in range(n-x+1): b1 = choose(z+1, y) * choose(x-1, y-1) a2 = 0 for j in range(n-z-x+1): a2 += (-1) ** j * choose(z+1+y, j) * choose(n-x-j-y, n-x-j-z) a1 += b1 * a2 return a1 Note that the choose function uses factorial, which I realize won't work for larger $N$ - but should be fine for $N=8$. [1] Counting Runs of Ones and Ones in Runs of Ones in Binary Strings, Frosso S. Makri, Zaharias M. Psillakis, Nikolaos Kollas https://file.scirp.org/pdf/OJAppS_2013011110241057.pdf [2] On success runs of a fixed length in Bernoulli sequences: Exact and asymptotic results, Frosso S.Makria, Zaharias M.Psillakis http://www.sciencedirect.com/science/article/pii/S0898122110009284
Ex-Celtic ace Chris Sutton hits back at Rangers troll with Progrès reference
Ex-Celtic ace Chris Sutton has hit back at a Rangers troll online by responding to his cheeky comment with one of his own be mentioning Progrès.
When Rangers played Celtic after the one minute did the Rangers boo back to the Celtic fans?
Have Dundee United's Insults At Rangers Been Forced Back Down Their Throats?
4 months ago Dundee United beat newco rangers 3-1 at Ibrox. Yesterday Celtic beat Dundee United 6-1.Does this show the massive gulf in class?
Is Celtic a bigger club than Rangers?
Ally McCoist took over from Walter Smith in June 2011 but season 2011–12 started with Rangers eliminated from two European competitions before the end of August: losing to Swedish side Malmö FF in the Champions League third round qualifying match, and to Slovenian side Maribor in a Europa League qualifying match. While good league form saw Rangers in top spot after being unbeaten for the first 15 games, they were knocked out of the League Cup by Falkirk and the Scottish Cup by Dundee Utd at Ibrox. Rangers was placed into administration on 14 February 2012 resulting in the club being deducted 10 points as per SPL rules. Though Rangers avoided having Celtic win the championship at Ibrox on 25 March by winning the game 3–2, Rangers ultimately finished 20 points behind Celtic in second place. A failure to reach agreement with creditors on 14 June 2012 led to The Rangers Football Club plc (since renamed RFC 2012 plc) entering the process of liquidation.
Rangers fan forced to visit Celtic store after Ibrox club shop runs out of letters for back of his strip
Andrew Grant had to make an embarrassing appearance 'behind enemy lines' to get Mr and Mrs Gers strips as a wedding present for his pal.
The Tetterbys were up, and doing. Mr. Tetterby took down the shutters of the shop, and, strip by strip, revealed the treasures of the window to the eyes, so proof against their seductions, of Jerusalem Buildings. Adolphus had been out so long already, that he was halfway on to “Morning Pepper.” Five small Tetterbys, whose ten round eyes were much inflamed by soap and friction, were in the tortures of a cool wash in the back kitchen; Mrs. Tetterby presiding. Johnny, who was pushed and hustled through his toilet with great rapidity when Moloch chanced to be in an exacting frame of mind (which was always the case), staggered up and down with his charge before the shop door, under greater difficulties than usual; the weight of Moloch being much increased by a complication of defences against the cold, composed of knitted worsted-work, and forming a complete suit of chain-armour, with a head-piece and blue gaiters.
America, feeling for the "Curiosity Shop" in, 19; projected visit to, 20; description of life in, 24; how Dickens was interviewed in, 26; amateur theatricals in, 28; friends in, 30, 238; voyage home from, 34; second visit of Dickens to, 234, 241, 244-249; Dickens's feeling for the people of, 237; the great walking-match in, 244; second journey home from, 249-252; desire on the part of Dickens to promote friendly relations between England and, 259; letters from, 24, 27, 28, 244-249
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