![](/files/happy5.png)
Tarsi, Michael
Coloring the union of degenerate graphs ★★
Author(s): Tarsi
Conjecture The union of a
-degenerate graph (a forest) and a
-degenerate graph is
-colourable.
![$ 1 $](/files/tex/f81bea742c6e484717a25f7b16835462361c1d2e.png)
![$ 2 $](/files/tex/5271e36bb1c040e0f14061d89cd97d0c86d4e06f.png)
![$ 5 $](/files/tex/87f5fe1d4b06035debb52cf2d67802fbfa9cb4ab.png)
Keywords:
Even vs. odd latin squares ★★★
A latin square is even if the product of the signs of all of the row and column permutations is 1 and is odd otherwise.
Conjecture For every positive even integer
, the number of even latin squares of order
and the number of odd latin squares of order
are different.
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
Keywords: latin square
The additive basis conjecture ★★★
Author(s): Jaeger; Linial; Payan; Tarsi
Conjecture For every prime
, there is a constant
(possibly
) so that the union (as multisets) of any
bases of the vector space
contains an additive basis.
![$ p $](/files/tex/928cd9d544fdea62f88a627aaee28c416c4366c0.png)
![$ c(p) $](/files/tex/996da72e7b0b6591ec8cc40dcbe46964d764e211.png)
![$ c(p)=p $](/files/tex/b1a6c0fbe5cae8582d2ef00c5f0f5158c9d9d4be.png)
![$ c(p) $](/files/tex/996da72e7b0b6591ec8cc40dcbe46964d764e211.png)
![$ ({\mathbb Z}_p)^n $](/files/tex/ea205f9e138abfc9a2c6a35332ecc6694ebe6419.png)
Keywords: additive basis; matrix
![Syndicate content Syndicate content](/misc/feed.png)