[seqfan] Re: A001495
israel at math.ubc.ca
israel at math.ubc.ca
Sun Aug 4 21:30:55 CEST 2013
Indeed. This sequence really needs a new title and some comments.
Cheers,
Robert
On Aug 4 2013, David Newman wrote:
>Thanks. I couldn't have understood that from the title.
>
>On Sun, Aug 4, 2013 at 1:52 PM, <israel at math.ubc.ca> wrote:
>
>> This seems to be what Gupta's article calls gamma^*(n+1), the number of
>> (n+1) x (n+1) symmetric 0-1 matrices with row sums 2 and first row
>> (1,1,0,...). Thus A(3) = 3 because there are 3 symmetric 4 x 4 0-1
>> matrices with row sums 2 and first row 1 1 0 0, namely
>>
>> 1100
>> 1001
>> 0011
>> 0110
>>
>> 1100
>> 1010
>> 0101
>> 0011
>>
>> and
>>
>> 1100
>> 1100
>> 0011
>> 0011
>>
>> Cheers,
>> Robert
>>
>>
>> On Aug 4 2013, David Newman wrote:
>>
>> This sequence is titled Number of Stochastic Matrices of Integers and it
>>> begins
>>>
>>> 1,1,1,3,13,70. I don't understand this. It seems to me that for n=2
>>> there are two matrices of non-negative integers with row sums 1 and
>>> column sums of 1, namely
>>>
>>> ((1,0),(0,1)) and ((0,1),(1,0)). So a(2) should be 2, not 1. There is
>>> a reference to an article called "Enumeration of Symmetric Matrices',
>>> but I don't have access to this. Can someone explain to me what is
>>> being counted by this sequence?
>>>
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