According to , a sestina is a highly structured poem consisting of six six-line stanzas followed by a tercet (called its envoy or tornada), for a total of thirty-nine lines. The same set of six words ends the lines of each of the six-line stanzas, but in a shuffled order each time. The shuffle used is very similar to the Mongean shuffle.
Define , if k <= n/2 and , if Let , where and is the symmetric group of order . From , we have the following result.
Theorem: If p is an n-cycle then 2n+1 is a prime.
Call such a prime a “sestina prime”. Which primes are sestina primes?
Here is Python/Sage code for this permutation:
def sestina(n): """ Computes the element of the symmetric group S_n associated to the shuffle above. EXAMPLES: sage: sestina(4) (1,2,4) sage: sestina(6) (1,2,4,5,3,6) sage: sestina(8) (1,2,4,8)(3,6,5,7) sage: sestina(10) (1,2,4,8,5,10)(3,6,9) sage: sestina(12) (1,2,4,8,9,7,11,3,6,12)(5,10) sage: sestina(14) (1,2,4,8,13,3,6,12,5,10,9,11,7,14) sage: sestina(16) (1,2,4,8,16)(3,6,12,9,15)(5,10,13,7,14) sage: sestina(18) (1,2,4,8,16,5,10,17,3,6,12,13,11,15,7,14,9,18) sage: sestina(20) (1,2,4,8,16,9,18,5,10,20)(3,6,12,17,7,14,13,15,11,19) sage: sestina(22) (1,2,4,8,16,13,19,7,14,17,11,22)(3,6,12,21)(5,10,20)(9,18) """ def fcn(k, n): if k<=int(n/2): return 2*k else: return 2*n+1-2*k L = [fcn(k,n) for k in range(1,n+1)] G = SymmetricGroup(n) return G(L)
And here is an example due to Ezra Pound :
I Damn it all! all this our South stinks peace. You whoreson dog, Papiols, come! Let’s to music! I have no life save when the swords clash. But ah! when I see the standards gold, vair, purple, opposing And the broad fields beneath them turn crimson, Then howl I my heart nigh mad with rejoicing. II In hot summer have I great rejoicing When the tempests kill the earth’s foul peace, And the light’nings from black heav’n flash crimson, And the fierce thunders roar me their music And the winds shriek through the clouds mad, opposing, And through all the riven skies God’s swords clash. III Hell grant soon we hear again the swords clash! And the shrill neighs of destriers in battle rejoicing, Spiked breast to spiked breast opposing! Better one hour’s stour than a year’s peace With fat boards, bawds, wine and frail music! Bah! there’s no wine like the blood’s crimson! IV And I love to see the sun rise blood-crimson. And I watch his spears through the dark clash And it fills all my heart with rejoicing And prys wide my mouth with fast music When I see him so scorn and defy peace, His lone might ’gainst all darkness opposing. V The man who fears war and squats opposing My words for stour, hath no blood of crimson But is fit only to rot in womanish peace Far from where worth’s won and the swords clash For the death of such sluts I go rejoicing; Yea, I fill all the air with my music. VI Papiols, Papiols, to the music! There’s no sound like to swords swords opposing, No cry like the battle’s rejoicing When our elbows and swords drip the crimson And our charges ’gainst “The Leopard’s” rush clash. May God damn for ever all who cry “Peace!” VII And let the music of the swords make them crimson Hell grant soon we hear again the swords clash! Hell blot black for always the thought “Peace”!
 Richard Dore and Anton Geraschenko,”Sestinas and Primes” posted to http://stacky.net/wiki/index.php?title=Course_notes, and http://math.berkeley.edu/~anton/written/sestina.pdf
 Ezra Pound, “Sestina: Altaforte” (1909), (originally published int the English Review, 1909)
 John Bullitt, N. J. A. Sloane and J. H. Conway , http://oeis.org/A019567